# Binary Spin Lattice

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## WHAT IS IT?

This is a model of a binary spin lattice thermodynamic system that measures properties such as temperature, entropy, total energy. The spins in the binary spin lattice system can either be up representing an excited state or can be down representing the ground state. These spins can be influenced and flipped by neighboring spins.

## HOW IT WORKS

In this model, the patches represent nuclei that are in different energy states. These energy states can change when influenced by neighboring patches. If most of neighboring patches are spin up or greater than zero, then the patch being influenced will flip up to the excited state and if this is not the case, then the patch will flip down to the ground state.

The model stops when the temperatures of the two spin groups have reached thermal equilibrium.

The switches will affect the outcome of thermodynamic properties, the world division switch makes one spin group large and the other spin group smaller.

The sliders will also affect the outcome of the simulation. Any percent extied slider above fifty will produce a negative temperature and any below will produce a positive temperature.

## HOW TO USE IT

SET UP: a button that resets the model and updates any changes made to the sliders and/or switches.

GO: a button that continually runs the simulation.

MONITORS: temp3 a, temp3 b, entropy3 a, entropy3 b, total entropy3, total energy3 a, total energy3 b, and total total energy3 are monitors in the interface that are updated while the simulation is running. The final measurements on the monitors reflect when both spin groups are at equilibrium with each other.

PERCENT EXCITED A: a slider that allows the percent of excited nuclei to vary for spin group a (blue group).

PERCENT EXCITED B: a slider that allows the percent of excited nuclei to vary for spin group b (pink group).

DENSE SETUP: a switch that splits the world in half creating spin group a and spin group b and allows the percent of excited nuclei of each spin group to be contained on either side of the world.

WORLD DIVISION: a switch that isolates spin group b in the bottom right corner which results in a larger spin group a.

PLOTS: these plots will continue to update throughout the simulation.

## THINGS TO NOTICE

When the spin group temperatures are transitioning from a positive temperature to a negative temperature or vice versa, the temp3 a and temp3 b plot will fluctuate between the boundary of positive infinity to negative infinity. The plot is discontinuous between the positive and negative infinites during this time because the program reads these values as extremely positive or extremely negative contrary to the kelvin scale where they are near each other.

## THINGS TO TRY

Analyze how the temperatures react when both switches are on and percent excited a is much greater then percent excited b as well as when percent excited a is much less than percent excited b. Compare and contrast the final data with different switch scenarios.

When both switches are on, try setting percent excited b two percents higher than percent excited a and determine why it only took less than five ticks to reach equilibrium. Also, vary delta e to determine if this slider increases or decreases the amount of ticks.

Next, try setting the percent excited's three values away from each other and manipulate delta e to compare the number of ticks it takes to reach equilibrium when both switches are on.

Observe the differences between having different switches on or off and how it affects the number of ticks to reach equilibrium.

## EXTENDING THE MODEL

- Creating a three-level system
- Changing the world division to occupy a larger or smaller space within the world thus enabling one group to act as a heat reservoir
- Modifying the world size of the spin groups
- Including the entropy of mixing

## RELATED MODELS

Ising Model (in the Chemistry & Physics - GasLab Section of Models Library)

## CREDITS AND REFERENCES

This model was created by Jennifer Campos and Kaitlyn Moore as part of Palm Beach Atlantic University's Summer UnderGraduate Academic Research (SUGAR) Program.

Credit to: Dr. Fred Browning for advising this modeling project

Wilensky, U. (2003). NetLogo Ising model. http://ccl.northwestern.edu/netlogo/models/Ising. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

### Additional resources that were used to complete this model:

Kelly, J. (1996-2002). Ensembles. http://www.physics.umd.edu/courses/Phys603/kelly/Notes/Ensembles.pdf. Statistical Physics using Mathmatica.

Kittel C. & Kroemer H. (1980). Thermal Physics, Second Edition. University of California, San Francisco. W. H. Freeman and Company, NY.

Railsback, S. F., & Grimm, V. (2012). Agent-based and individual-based modeling: A practical introduction. Princeton, N.J: Princeton University Press.

Klein, M. (1956) Thermodynamics and Statistical Mechanics at Negative Absolute Temperatures. Physical Review, 103, 20-28.

Section 2: Introduction to Statistical Mechanics. (1997). http://personal.rhul.ac.uk/uhap/027/ph2610/ph2610_files/sect2.pdf.

Wikipedia Contributors. (3 June 2017). Population Inversion. https://en.wikipedia.org/wiki/Population_inversion. Wikipedia, The Free Encyclopedia.

## Comments and Questions

globals [ ; variables for spin groups a (blue) and spin group b (pink) spin_diff_a ; difference between spin ups(e two's) and spin downs(e one's) in spin group a spin_diff_b ; difference between spin ups and spin downs in spin group b n_two_a ; excited state for spin group a (dark blue) n_two_b ; excited state for spin group b (dark pink) n_one_a ; ground state for spin group a (light blue) n_one_b ; ground state for spin group b (light pink) total_energy_a ; spin group a's total energy total_energy_b ; spin group b's total energy e_one_a ; spin downs for spin group a (blue) when negative e_one_b ; spin downs for spin group b (pink) when negative e_two_a ; spin ups for spin group a (blue) when positive e_two_b ; spin ups for spin group b (pink) when positve n_total_a ; total number of spins in group a n_total_b ; total number of spins in group b entropy_a entropy_b temperature2_a temperature2_b free_energy_a free_energy_b delta_e_b spin_group_a ; left side of the world in blue spin_group_b ; right side of the world in pink temp_hold_a ; compares previous step of spin group a and stops temperatures from crossing and flipping temp_hold_b ; compares previous step of spin group b and stops temperatures from crossing and flipping spin_flip_a ; keeps track on whether or not more than 50% of a spin group is exctied spin_flip_b spin_flip_hold_a ; compares previous step of spin group a and stops temperatures from crossing and flipping spin_flip_hold_b ; compares previous step of spin group b and stops temperatures from crossing and flipping ; ] patches-own [spin ; holds 1 or 2 orientation ; -1 or 1 for spin 1 or 2 respectively spin_group ; spin group a = 1 is blue and spin group b = 2 is pink ] to setup ca ; resets all global variables to zero set e_one_a 100 ; ground state energy for spin group a (blue) set e_one_b 100 ; ground state energy for spin group b (pink) set delta_e_b delta_e_a ; set the same enregy difference for both spin groups set e_two_a (e_one_a + delta_e_a) ; excited state energy for spin group a set e_two_b (e_one_b + delta_e_b) ; excited state energy for spin group b ask patches [set spin 1 ; sets all to ground state (spin down) set orientation -1] ; sets all to ground state (spin down) if dense-setup = true and world-division = true [setup1] if dense-setup = false and world-division = false [setup2] if dense-setup = true and world-division = false [setup3] if dense-setup = false and world-division = true [setup4] reset-ticks ; resets ticks to zero and resets plots end to setup1 ; when both switches are on nuclei are contained and are distrubuted ; and world-division = true if world-division = true [ ; into rectangular blocks based on the amount of percent excited set set n_two_a ceiling ((percent_excited_a / 100) * (0.75 * world-width * world-height)) ; sets spin group a larger set n_two_b ceiling ((percent_excited_b / 100) * (0.25 * world-width * world-height))] ; sets spin group b smaller set n_one_a floor ((world-width * world-height) - n_two_a) set n_one_b floor ((world-width * world-height) - n_two_b) set n_total_a floor (n_one_a + n_two_a) set n_total_b floor (n_one_b + n_two_b) ask patches [set spin_group 1 set pcolor blue] ask patches [if pxcor >= world-width / 2 and pycor <= (world-height / 2) [set spin_group 2 set pcolor pink] ] if dense-setup = true [ set n_two_a ceiling ((percent_excited_a / 100) * (0.75 * world-width * world-height)) set n_two_b ceiling ((percent_excited_b / 100) * (0.25 * world-width * world-height)) let bw (world-width / 4) ; sets block width where world is divided into 4 x 4 rectangles let bh (world-height / 4) ; sets block height where world is divided into 4 x 4 rectangles let block_area floor ((world-width / 4) * (world-height / 4)) ; area of one rectanlge block let number_b_blocks ceiling (n_two_b / block_area) ; determines number of blocks for spin group b let number_a_blocks ceiling (n_two_a / block_area) ; determines number of blocks for spin group a ; sets rectangular sections for spin group a if number_a_blocks = 1 [ask n-of n_two_a patches with [pxcor < (bw) and pycor <= (bh)] [set spin 2 set orientation 1]] if number_a_blocks = 2 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh)) or (pxcor < (bw) and pycor <= ((bh * 2) ))] [set spin 2 set orientation 1]] if number_a_blocks = 3 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh)) or (pxcor < (bw) and pycor <= ((bh * 2))) or (pxcor < (bw) and pycor <= ((bh * 3)))] [set spin 2 set orientation 1]] if number_a_blocks = 4 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh)) or (pxcor < (bw) and pycor <= ((bh * 2))) or (pxcor < (bw) and pycor <= ((bh * 3))) or (pxcor < (bw) and pycor <= ((bh * 4)))] [set spin 2 set orientation 1]] if number_a_blocks = 5 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (2 * bw) and pycor > (3 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 6 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (3 * bw) and pycor >= (3 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 7 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 8 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh)) or (pxcor < (bw * 2) and pycor <= (bh))] [set spin 2 set orientation 1]] if number_a_blocks = 9 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh)) or (pxcor < (bw * 2) and pycor <= (2 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 10 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh)) or (pxcor < (bw * 2) and pycor <= (3 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 11 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh)) or (pxcor < (bw * 2) and pycor < (3 * bh)) or (pxcor < (3 * bw) and pycor >= (2 * bh))] [set spin 2 set orientation 1]] if number_a_blocks = 12 [ask n-of n_two_a patches with [(pxcor < (bw) and pycor <= (bh * 4)) or (pxcor < (4 * bw) and pycor >= (3 * bh)) or (pxcor < (bw * 2) and pycor <= (3 * bh)) or (pxcor < (4 * bw) and pycor > (2 * bh))] [set spin 2 set orientation 1]] ; sets rectangular sections for spin group b if number_b_blocks = 1 [ask n-of n_two_b patches with [pxcor > ((3 * bw) - 1) and pycor <= (bh - 1)] [set spin 2 set orientation 1]] if number_b_blocks = 2 [ask n-of n_two_b patches with [(pxcor > ((3 * bw) - 1) and pycor <= (bh - 1)) or (pxcor > ((2 * bw) - 1) and pycor <= (bh - 1))] [set spin 2 set orientation 1]] if number_b_blocks = 3 [ask n-of n_two_b patches with [(pxcor > ((3 * bw) - 1) and pycor <= (bh - 1)) or (pxcor > ((2 * bw) - 1) and pycor <= (bh - 1)) or (pxcor > ((3 * bw) - 1) and pycor <= (2 * bh))] [set spin 2 set orientation 1]] if number_b_blocks = 4 [ask n-of n_two_b patches with [(pxcor > ((3 * bw) - 1) and pycor <= (bh - 1)) or (pxcor > ((2 * bw) - 1) and pycor <= (bh - 1)) or (pxcor > ((3 * bw) - 1) and pycor <= (2 * bh)) or (pxcor >= ((2 * bw)) and pycor <= (2 * bh))] [set spin 2 set orientation 1]] set spin_diff_a count patches with [spin = 2 and spin_group = 1] - count patches with [spin = 1 and spin_group = 1] set spin_diff_b count patches with [spin = 2 and spin_group = 2] - count patches with [spin = 1 and spin_group = 2] set temperature2_a temp2_a set temperature2_b temp2_b set entropy_a S_a set entropy_b S_b set total_energy_a U_a set total_energy_b U_b set free_energy_a F_a set free_energy_b F_b set temp_hold_a temp3_a set temp_hold_b temp3_b ; if most of neighbor patches are spin up (greater than 0) then set spint_flip 1 and if not se spin_flip 0 ifelse (spin_diff_a > 0) [set spin_flip_a 1] [ifelse (spin_diff_a < 0) [set spin_flip_a -1][set spin_flip_a 0] ] ifelse (spin_diff_b > 0) [set spin_flip_b 1] [ifelse (spin_diff_b < 0) [set spin_flip_b -1][set spin_flip_b 0] ] ask patches [recolor] ] end to setup2 ; when both switches are fasle world is if world-division = false [ ; cut in half and nuclei are spread out set n_two_a floor ((percent_excited_a / 100) * (0.5 * world-width * world-height)) set n_two_b floor ((percent_excited_b / 100) * (0.5 * world-width * world-height))] set n_one_a floor ((world-width * world-height) - n_two_a) set n_one_b floor ((world-width * world-height) - n_two_b) set n_total_a floor (n_one_a + n_two_a) set n_total_b floor (n_one_b + n_two_b) ask patches [set spin_group 1 set pcolor blue] ask patches [if pxcor > (world-width / 2 - 1) [set pcolor pink set spin_group 2] ] if dense-setup = false [ ask n-of n_two_a patches with [spin_group = 1] [set spin 2 ; excited states in spin group a (dark blue) set orientation 1] ask n-of n_two_b patches with [spin_group = 2] [set spin 2 ; excited states in spin group b (dark pink) set orientation 1] ask patches [recolor] ; sets color of the spins that determine excited or ground states set spin_diff_a count patches with [spin = 2 and spin_group = 1] - count patches with [spin = 1 and spin_group = 1] set spin_diff_b count patches with [spin = 2 and spin_group = 2] - count patches with [spin = 1 and spin_group = 2] set temperature2_a temp2_a set temperature2_b temp2_b set entropy_a S_a set entropy_b S_b set total_energy_a U_a set total_energy_b U_b set free_energy_a F_a set free_energy_b F_b set temp_hold_a temp3_a set temp_hold_b temp3_b ifelse (spin_diff_a > 0) [set spin_flip_a 1] [ifelse (spin_diff_a < 0) [set spin_flip_a -1][set spin_flip_a 0] ] ifelse (spin_diff_b > 0) [set spin_flip_b 1] [ifelse (spin_diff_b < 0) [set spin_flip_b -1][set spin_flip_b 0] ] ] end to setup3 ; when world division switch is if world-division = false [ ; false the world is cut in half set n_two_a floor ((percent_excited_a / 100) * (0.5 * world-width * world-height)) set n_two_b floor ((percent_excited_b / 100) * (0.5 * world-width * world-height))] set n_one_a floor ((world-width * world-height) - n_two_a) set n_one_b floor ((world-width * world-height) - n_two_b) set n_total_a floor (n_one_a + n_two_a) set n_total_b floor (n_one_b + n_two_b) ask patches [set spin_group 1 set pcolor blue] ask patches [if pxcor > (world-width / 2 - 1) [set pcolor pink set spin_group 2] ] if dense-setup = true [ let x_excited_a floor ((percent_excited_a / 100) * (world-width / 2)) let x_excited_b ceiling (world-width - (percent_excited_b / 100) * (world-width / 2)) ask n-of n_two_a patches with [pxcor <= x_excited_a] [set spin 2 set orientation 1] ask n-of n_two_b patches with [ pxcor >= x_excited_b - 1 ][set spin 2 set orientation 1] set spin_diff_a count patches with [spin = 2 and spin_group = 1] - count patches with [spin = 1 and spin_group = 1] set spin_diff_b count patches with [spin = 2 and spin_group = 2] - count patches with [spin = 1 and spin_group = 2] set temperature2_a temp2_a set temperature2_b temp2_b set entropy_a S_a set entropy_b S_b set total_energy_a U_a set total_energy_b U_b set free_energy_a F_a set free_energy_b F_b set temp_hold_a temp3_a set temp_hold_b temp3_b ifelse (spin_diff_a > 0) [set spin_flip_a 1] [ifelse (spin_diff_a < 0) [set spin_flip_a -1][set spin_flip_a 0] ] ifelse (spin_diff_b > 0) [set spin_flip_b 1] [ifelse (spin_diff_b < 0) [set spin_flip_b -1][set spin_flip_b 0] ] ask patches [recolor] ] end to setup4 if world-division = true [ set n_two_a floor ((percent_excited_a / 100) * (0.75 * world-width * world-height)) set n_two_b floor ((percent_excited_b / 100) * (0.25 * world-width * world-height))] set n_one_a floor ((world-width * world-height) - n_two_a) set n_one_b floor ((world-width * world-height) - n_two_b) set n_total_a floor (n_one_a + n_two_a) set n_total_b floor (n_one_b + n_two_b) ask patches [set spin_group 1 set pcolor blue] ask patches [if (pxcor >= world-width / 2) and (pycor <= world-height / 2) [set spin_group 2 set pcolor pink] ] if dense-setup = false [ ask n-of n_two_a patches with [spin_group = 1] [set spin 2 set orientation 1] ask n-of n_two_b patches with [spin_group = 2] [set spin 2 set orientation 1] ask patches [recolor] set spin_diff_a count patches with [spin = 2 and spin_group = 1] - count patches with [spin = 1 and spin_group = 1] set spin_diff_b count patches with [spin = 2 and spin_group = 2] - count patches with [spin = 1 and spin_group = 2] set temperature2_a temp2_a set temperature2_b temp2_b set entropy_a S_a set entropy_b S_b set total_energy_a U_a set total_energy_b U_b set free_energy_a F_a set free_energy_b F_b set temp_hold_a temp3_a set temp_hold_b temp3_b ifelse (spin_diff_a > 0) [set spin_flip_a 1] [ifelse (spin_diff_a < 0) [set spin_flip_a -1][set spin_flip_a 0] ] ifelse (spin_diff_b > 0) [set spin_flip_b 1] [ifelse (spin_diff_b < 0) [set spin_flip_b -1][set spin_flip_b 0] ] ] end to recolor ; colors patches according to spin ifelse spin_group = 1 [ ifelse spin = 1 [set pcolor blue + 2] ; excited state for spin group a [set pcolor blue - 2] ; ground state for spin group a ] [ifelse spin = 1 [set pcolor pink + 2] ; excited state for spin group b [set pcolor pink - 2] ; ground state for spin group b ] end to go repeat 1000 [ ; updates 1000 patches at a time ask one-of patches [update] ] set spin_diff_a count patches with [spin = 2 and spin_group = 1] - count patches with [spin = 1 and spin_group = 1] set spin_diff_b count patches with [spin = 2 and spin_group = 2] - count patches with [spin = 1 and spin_group = 2] tick ; updating 1000 patches at a time only update-plots ; must update plots separately if floor temp3_a = floor temp3_b [stop] ; rounding values to if floor temp3_a = ceiling temp3_b [stop] ; show that equilibrium if ceiling temp3_a = floor temp3_b [stop] ; has been reached if ticks > 50000 [stop] ; if equilibrium has not been reached yet ifelse (spin_diff_a > 0) [set spin_flip_a 1 ] [ifelse (spin_diff_a < 0) [set spin_flip_a -1][set spin_flip_a 0] ] ifelse (spin_diff_b > 0) [set spin_flip_b 1] [ifelse (spin_diff_b < 0) [set spin_flip_b -1][set spin_flip_b 0] ] if (spin_flip_hold_a = spin_flip_a and spin_flip_hold_b = spin_flip_b) [ ; when temp3_a and temp3_b cross if (temp3_a < temp3_b and temp_hold_a > temp_hold_b) [stop] if (temp3_a > temp3_b and temp_hold_a < temp_hold_b) [stop] ] set temp_hold_a temp3_a set temp_hold_b temp3_b set spin_flip_hold_a spin_flip_a set spin_flip_hold_b spin_flip_b end to update ; updating spins of one patch let Ediff (2 * orientation * sum [orientation] of neighbors) if (Ediff <= 0) [ let hold_orientation orientation ask n-of 1 neighbors with [orientation != hold_orientation] [ ; if neighboring spins are different then changes to ground state set orientation (- orientation) ifelse orientation = -1 [set spin 1] [set spin 2] ; if true then ground state and if not assign to excited state recolor ] set orientation (- orientation) ifelse orientation = -1 [set spin 1] [set spin 2] recolor ] end to-report S_a ; spin group a initial entropy report (1) * (n_total_a * ln (n_total_a) - n_two_a * ln (n_two_a) - n_one_a * ln (n_one_a)) end to-report S_b ; spin group b initial entropy report (1) * (n_total_b * ln (n_total_b) - n_two_b * ln (n_two_b) - n_one_b * ln (n_one_b)) end to-report entropy3_a ; updates monitor report (1) * (n_total_a * ln (n_total_a) - count patches with [spin = 2 and spin_group = 1] * ln (count patches with [spin = 2 and spin_group = 1]) - count patches with [spin = 1 and spin_group = 1] * ln (count patches with [spin = 1 and spin_group = 1])) end to-report entropy3_b ; updates monitor report (1) * (n_total_b * ln (n_total_b) - count patches with [spin = 2 and spin_group = 2] * ln (count patches with [spin = 2 and spin_group = 2]) - count patches with [spin = 1 and spin_group = 2] * ln (count patches with [spin = 1 and spin_group = 2])) end to-report total_entropy3 ; updates monitor report (1) * (n_total_a * ln (n_total_a) - count patches with [spin = 2 and spin_group = 1] * ln (count patches with [spin = 2 and spin_group = 1]) - count patches with [spin = 1 and spin_group = 1] * ln (count patches with [spin = 1 and spin_group = 1])) + (1) * (n_total_b * ln (n_total_b) - count patches with [spin = 2 and spin_group = 2] * ln (count patches with [spin = 2 and spin_group = 2]) - count patches with [spin = 1 and spin_group = 2] * ln (count patches with [spin = 1 and spin_group = 2])) end to-report U_a ; initial total_energy report ((n_two_a * e_two_a) + (n_one_a * e_one_a)) end to-report U_b ; initial total_energy report ((n_two_b * e_two_b) + (n_one_b * e_one_b)) end to-report total_energy3_a ; updates monitor report ((count patches with [spin = 2 and spin_group = 1] * e_two_a) + (count patches with [spin = 2 and spin_group = 2] * e_one_a)) end to-report total_energy3_b ; updates monitor report ((count patches with [spin = 2 and spin_group = 2] * e_two_b) + (count patches with [spin = 1 and spin_group = 2] * e_one_b)) end to-report total_total_energy3 ; updates monitor report ((count patches with [spin = 2 and spin_group = 1] * e_two_a) + (count patches with [spin = 2 and spin_group = 2] * e_one_a)) + ((count patches with [spin = 2 and spin_group = 2] * e_two_b) + (count patches with [spin = 1 and spin_group = 2] * e_one_b)) end to-report temp2_a ; initial temperature ifelse (n_two_a / n_one_a) = 1 [report 0] [ report ( -1 * (e_two_a - e_one_a) / (ln (n_two_a / n_one_a)))] end to-report temp2_b ; initial temperature ifelse (n_two_b / n_one_b) = 1 [report 0] [ report ( -1 * (e_two_b - e_one_b) / (ln (n_two_b / n_one_b)))] end to-report temp3_a ; updates monitor ifelse (count patches with [spin = 2 and spin_group = 1] / count patches with [spin = 1 and spin_group = 1]) = 1 [report 0] [ report ( -1 * (e_two_a - e_one_a) / (ln (count patches with [spin = 2 and spin_group = 1] / count patches with [spin = 1 and spin_group = 1])))] end to-report temp3_b ; updates monitor ifelse (count patches with [spin = 2 and spin_group = 2] / count patches with [spin = 1 and spin_group = 2]) = 1 [report 0] [ report ( -1 * (e_two_b - e_one_b) / (ln (count patches with [spin = 2 and spin_group = 2] / count patches with [spin = 1 and spin_group = 2])))] end to-report F_a ; initial free_energy report (total_energy_a - (temperature2_a * entropy_a)) end to-report F_b ; initial free_energy report (total_energy_b - (temperature2_b * entropy_b)) end

There are 2 versions of this model.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

Binary Spin Lattice.png | preview | Preview for 'Binary Spin Lattice' | over 5 years ago, by Fred Browning | Download |

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