User contributions for Hhc16

19:3219:32, 20 November 2018 diff hist +10 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
19:2919:29, 20 November 2018 diff hist +3 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
19:2419:24, 20 November 2018 diff hist +261 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
19:1719:17, 20 November 2018 diff hist +140 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 show...
19:1519:15, 20 November 2018 diff hist +812 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 six columns: T, E, E^2, M, M^2, C (the final...
18:2918:29, 20 November 2018 diff hist −1 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
18:2218:22, 20 November 2018 diff hist −2 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: By definition, C = \frac{\partial \left\langle E\right\rangle}{\partial T}. From this, show that C = \frac{\mathrm{Var}[E]}{k_B T^2}. Where \mathrm{Var}[E] is the variance in E.
18:2118:21, 20 November 2018 diff hist +1 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: By definition, C = \frac{\partial \left\langle E\right\rangle}{\partial T}. From this, show that C = \frac{\mathrm{Var}[E]}{k_B T^2}. Where \mathrm{Var}[E] is the variance in E.
18:2018:20, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) →The Heat Capacity
18:1918:19, 20 November 2018 diff hist −1 Rep:Simulations of a 2D Ising Model (hhc16) →TASK: By definition, C = \frac{\partial \left\langle E\right\rangle}{\partial T}. From this, show that C = \frac{\mathrm{Var}[E]}{k_B T^2}. Where \mathrm{Var}[E] is the variance in E.
18:1918:19, 20 November 2018 diff hist +1 Rep:Simulations of a 2D Ising Model (hhc16) →The Heat Capacity
18:1818:18, 20 November 2018 diff hist −16 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Complete the functions energy() and magnetisation(), which should return the energy of the lattice and the total magnetisation, respectively. In the energy() function you may assume that J=1.0 at all times. The efficiency of the code will be...
18:1718:17, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
18:1518:15, 20 November 2018 diff hist +96 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 show...
18:1318:13, 20 November 2018 diff hist +17 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 show...
18:1218:12, 20 November 2018 diff hist −2 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
18:1118:11, 20 November 2018 diff hist +1,756 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Use ILtemperaturerange.py to plot the average energy and magnetisation for each temperature, with error bars, for an 8\times 8 lattice. Use your intuition and results from the script ILfinalframe.py to estimate how many cycles each simulation...
17:5017:50, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 a...
17:4817:48, 20 November 2018 diff hist 0 N File:Firstorder HHSC.png No edit summary current
17:4817:48, 20 November 2018 diff hist +109 Rep:Simulations of a 2D Ising Model (hhc16) →The Heat Capacity
17:4717:47, 20 November 2018 diff hist +126 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
17:1217:12, 20 November 2018 diff hist +255 Rep:Simulations of a 2D Ising Model (hhc16) →The Heat Capacity
16:5116:51, 20 November 2018 diff hist +62 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 show...
16:4116:41, 20 November 2018 diff hist +289 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Write a Python script to make a plot showing the heat capacity versus temperature for each of your lattice sizes from the previous section. You may need to do some research to recall the connection between the variance of a variable, \mathrm{V...
16:0016:00, 20 November 2018 diff hist +16 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 a...
15:5715:57, 20 November 2018 diff hist +129 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...
15:5015:50, 20 November 2018 diff hist +209 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...
15:4315:43, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) →Introduction
15:4215:42, 20 November 2018 diff hist +303 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...
15:3315:33, 20 November 2018 diff hist +128 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
15:2715:27, 20 November 2018 diff hist 0 File:Metastable.gif Hhc16 uploaded a new version of File:Metastable.gif current
14:5914:59, 20 November 2018 diff hist 0 File:Metastable.gif Hhc16 uploaded a new version of File:Metastable.gif
14:5414:54, 20 November 2018 diff hist 0 File:Latticeanimate.gif Hhc16 uploaded a new version of File:Latticeanimate.gif current
14:5314:53, 20 November 2018 diff hist 0 File:Latticeanimate.gif Hhc16 uploaded a new version of File:Latticeanimate.gif
14:4914:49, 20 November 2018 diff hist +16 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: Look at the documentation for the NumPy sum function. You should be able to modify your magnetisation() function so that it uses this to evaluate M. The energy is a little trickier. Familiarise yourself with the NumPy roll and multiply functio...
14:4814:48, 20 November 2018 diff hist −5 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...
14:4814:48, 20 November 2018 diff hist +2 Rep:Simulations of a 2D Ising Model (hhc16) →Modifying IsingLattice.py
14:4614:46, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
14:4614:46, 20 November 2018 diff hist +6 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
14:4514:45, 20 November 2018 diff hist −6 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
14:4314:43, 20 November 2018 diff hist +7 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
14:4314:43, 20 November 2018 diff hist 0 N File:Latticeanimate.gif No edit summary
14:3614:36, 20 November 2018 diff hist 0 File:ANIMATE.gif Hhc16 uploaded a new version of File:ANIMATE.gif current
14:3314:33, 20 November 2018 diff hist 0 File:ANIMATE.gif Hhc16 uploaded a new version of File:ANIMATE.gif
14:3114:31, 20 November 2018 diff hist +1 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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()...
14:3014:30, 20 November 2018 diff hist 0 N File:ANIMATE.gif No edit summary
14:2614:26, 20 November 2018 diff hist 0 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...
14:2614:26, 20 November 2018 diff hist 0 N File:Metastable.gif No edit summary
14:2414:24, 20 November 2018 diff hist 0 N File:ILanim.gif No edit summary current
14:2314:23, 20 November 2018 diff hist −5 Rep:Simulations of a 2D Ising Model (hhc16) /* TASK: 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 ou...

20 November 2018