User contributions for Sw4512

15:0015:00, 9 February 2015 diff hist +40 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
15:0015:00, 9 February 2015 diff hist 0 N File:Linearfit.png No edit summary current
14:2714:27, 9 February 2015 diff hist +29 User:Sw4512cmp /* Repeat the final task of the previous section for the following lattice sizes: 2x2, 4x4, 8x8, 16x16, 32x32. Make sure that you name each datafile that your produce after the corresponding lattice size! Write a Python script to make a plot showing th...
13:2713:27, 9 February 2015 diff hist +22 User:Sw4512cmp /* II).Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the sy...
13:2613:26, 9 February 2015 diff hist −23 User:Sw4512cmp /* II).Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the sy...
13:2313:23, 9 February 2015 diff hist +198 User:Sw4512cmp /* find the temperature at which the maximum in C occurs for each datafile that you were given. Make a text file containing two colums: the lattice side length (2,4,8, etc.), and the temperature at which C is a maximum. This is your estimate of T_C for...
13:0213:02, 9 February 2015 diff hist 0 N File:32 sw4512.png No edit summary current
13:0213:02, 9 February 2015 diff hist 0 N File:16 sw4512.png No edit summary current
13:0213:02, 9 February 2015 diff hist 0 N File:8 sw4512.png No edit summary current
13:0213:02, 9 February 2015 diff hist 0 N File:4 sw4512.png No edit summary current
13:0113:01, 9 February 2015 diff hist 0 N File:2 sw4512.png No edit summary current
12:3412:34, 9 February 2015 diff hist +73 User:Sw4512cmp →Modify your script from the previous section. You should still plot the whole temperature range, but fit the polynomial only to the peak of the heat capacity! You should find it easier to get a good fit when restricted to this region.
12:3312:33, 9 February 2015 diff hist 0 N File:Partfitzoom.png No edit summary current
12:3312:33, 9 February 2015 diff hist 0 N File:Partfit.png No edit summary current
12:3212:32, 9 February 2015 diff hist +21 User:Sw4512cmp /* write a script to read the data from a particular file, and plot C vs T, as well as a fitted polynomial. Try changing the degree of the polynomial to improve the fit — in general, it might be difficult to get a good fit! Attach a PNG of an exa...
12:3112:31, 9 February 2015 diff hist 0 User:Sw4512cmp /* write a script to read the data from a particular file, and plot C vs T, as well as a fitted polynomial. Try changing the degree of the polynomial to improve the fit — in general, it might be difficult to get a good fit! Attach a PNG of an exa...
12:3112:31, 9 February 2015 diff hist +88 User:Sw4512cmp /* write a script to read the data from a particular file, and plot C vs T, as well as a fitted polynomial. Try changing the degree of the polynomial to improve the fit — in general, it might be difficult to get a good fit! Attach a PNG of an exa...
12:3112:31, 9 February 2015 diff hist 0 N File:Fullfit442.png No edit summary current
12:3112:31, 9 February 2015 diff hist 0 N File:Fullfit441.png No edit summary current
12:3012:30, 9 February 2015 diff hist 0 N File:Fullfit.png No edit summary current

17:4517:45, 2 February 2015 diff hist +1 User:Sw4512cmp /* II).Imagine that the system is in the lowest energy configuration. To move to a different state, one of the spins must spontaneously change direction ("flip"). What is the change in energy if this happens (D=3,\ N=1000)? How much entropy does the sy...
13:2713:27, 2 February 2015 diff hist +1 User:Sw4512cmp →complete the functions energy() and magnetisation(), which should return the energy of the lattice and the total magnetisation, respectively. export the figure as a PNG image
13:2513:25, 2 February 2015 diff hist −3 User:Sw4512cmp →I).Show that the lowest possible energy for the Ising model is E = -DNJ.
13:2513:25, 2 February 2015 diff hist −261 User:Sw4512cmp /* Use the script ILtimetrial.py to record how long your new version of IsingLattice.py takes to perform 2000 Monte Carlo steps. This will vary, depending on what else the computer happens to be doing, so perform repeats and report the error in your av...
13:2413:24, 2 February 2015 diff hist −145 User:Sw4512cmp /* Performance comparison Use the script ILtimetrial.py to record how long your current version of IsingLattice.py takes to perform 2000 Monte Carlo steps. This will vary, depending on what else the computer happens to be doing, so perform repeats and...
13:2313:23, 2 February 2015 diff hist +476 User:Sw4512cmp /* Performance comparison Use the script ILtimetrial.py to record how long your current version of IsingLattice.py takes to perform 2000 Monte Carlo steps. This will vary, depending on what else the computer happens to be doing, so perform repeats and...
12:1212:12, 2 February 2015 diff hist +6 User:Sw4512cmp /* A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains five columns: T, E, E^2, M, M^2, C_V, and you can...
12:1212:12, 2 February 2015 diff hist +903 User:Sw4512cmp /* A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains five columns: T, E, E^2, M, M^2, C_V, and you can...
12:0912:09, 2 February 2015 diff hist +11 User:Sw4512cmp /* Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy() functi...
12:0812:08, 2 February 2015 diff hist +64 User:Sw4512cmp /* Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy() functi...
12:0712:07, 2 February 2015 diff hist +13 User:Sw4512cmp /* Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy() function
12:0612:06, 2 February 2015 diff hist +3,742 User:Sw4512cmp /* Implement a single cycle of the above algorithm in the montecarlocycle(T) function. This function should return the energy of your lattice and the magnetisation at the end of the cycle. You may assume that the energy returned by your energy() functi...
11:5511:55, 2 February 2015 diff hist +22 User:Sw4512cmp /* Use the script ILtimetrial.py to record how long your current version of IsingLattice.py takes to perform 2000 Monte Carlo steps. This will vary, depending on what else the computer happens to be doing, so perform repeats and report the error in you...
11:5411:54, 2 February 2015 diff hist +136 User:Sw4512cmp →Magnetisation Calculations

19:1119:11, 1 February 2015 diff hist +5 User:Sw4512cmp /* Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your initution and results from the script ILfinalframe.py to estimate how many cycles each simulation should...
19:1019:10, 1 February 2015 diff hist −34 User:Sw4512cmp /* The script ILfinalframe.py runs for a given number of cycles at a given temperature, then plots a depiction of the final lattice state as well as graphs of the energy and magnetisation as a function of cycle number. This is much quicker than animati...
19:0819:08, 1 February 2015 diff hist −12 User:Sw4512cmp /* If T , do you expect a spontaneous magnetisation (i.e. do you expect \left\langle M\right\rangle \neq 0)? When the state of the simulation appears to stop changing (when you have reached an equilibrium state), use the controls to export the output t...
19:0519:05, 1 February 2015 diff hist −13 User:Sw4512cmp /* If T , do you expect a spontaneous magnetisation (i.e. do you expect \left\langle M\right\rangle \neq 0)? When the state of the simulation appears to stop changing (when you have reached an equilibrium state), use the controls to export the output t...
19:0519:05, 1 February 2015 diff hist −1 User:Sw4512cmp →The need for significance sampling?
19:0419:04, 1 February 2015 diff hist −252 User:Sw4512cmp /* How many configurations are available to a system with 100 spins? To evaluate these expressions, we have to calculate the energy and magnetisation and each of these configurations, then perform the sum. Let's be very, very, generous, and say that we...
19:0119:01, 1 February 2015 diff hist −6 User:Sw4512cmp →complete the functions energy() and magnetisation(), which should return the energy of the lattice and the total magnetisation, respectively. export the figure as a PNG image
18:5918:59, 1 February 2015 diff hist +1 User:Sw4512cmp →Magnetisation Calculations
18:5918:59, 1 February 2015 diff hist −142 User:Sw4512cmp →Calculate the magnetisation of the 1D and 2D lattices in figure 1. What magnetisation would you expect to observe for an Ising lattice with D=3, N=1000 at absolute zero?
18:5818:58, 1 February 2015 diff hist −135 User:Sw4512cmp →I).Show that the lowest possible energy for the Ising model is E = -DNJ, where D is the number of dimensions and N is the total number of spins. What is the multiplicity of this state? Calculate its entropy.
18:5518:55, 1 February 2015 diff hist −87 User:Sw4512cmp /* A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains five columns: T, E, E^2, M, M^2, C_V, and you can...
18:5018:50, 1 February 2015 diff hist +451 User:Sw4512cmp /* A C++ program has been used to run some much longer simulations than would be possible on the college computers in Python. You can view its source code here if you are interested. Each file contains five columns: T, E, E^2, M, M^2, C_V, and you can...
15:3615:36, 1 February 2015 diff hist 0 N File:2x2hc sw4512.png No edit summary current
15:3615:36, 1 February 2015 diff hist 0 N File:4x4heatcap sw4512.png No edit summary current
15:3515:35, 1 February 2015 diff hist 0 N File:8x8heatcap sw4512.png No edit summary current
15:3515:35, 1 February 2015 diff hist 0 N File:16x16heatcap sw4512.png No edit summary current

9 February 2015

2 February 2015

1 February 2015