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06: Tidy up some more, comment on transition

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Kees van Kempen
2022-10-18 22:17:31 +02:00
parent 084e31ad14
commit 38661216a0
1 changed files with 53 additions and 45 deletions
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Exercise sheet 6/exercise_sheet_06.ipynb
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@ -439,7 +439,7 @@
"\tequilibrating took 1.5426356792449951 seconds\n",
"\tmeasuring took 3.485330104827881 seconds\n",
"\n",
"T = 1.2000000000000002\n",
"T = 1.2\n",
"\tequilibrating took 0.4475827217102051 seconds\n",
"\tmeasuring took 1.3380379676818848 seconds\n",
"\n",
@ -486,19 +486,19 @@
" \n",
" for idx, T in enumerate(temperatures):\n",
" toc()\n",
" print(\"T =\", T)\n",
" print(\"T = {:.1f}\".format(T))\n",
" beta = 1/T\n",
" \n",
" # Equilibrate\n",
" for _ in range(equilibration_moves):\n",
" xy_cluster_move(state,beta)\n",
" print(\"\\tequilibrating took\", toc(), \" seconds\")\n",
" print(\"\\tequilibrating took {:2.3f} seconds\".format(toc()))\n",
" \n",
" # Measure\n",
" for _ in range(measurement_moves):\n",
" cluster_sizes[idx] += np.norm(xy_cluster_move(state,beta))\n",
" cluster_sizes[idx] += xy_cluster_move(state,beta)\n",
" cluster_sizes[idx] /= measurement_moves\n",
" print(\"\\tmeasuring took\", toc(), \" seconds\")\n",
" print(\"\\tmeasuring took {:2.3f} seconds\".format(toc()))\n",
" print()\n",
" \n",
" f.create_dataset(\"cluster-size\",data=cluster_sizes)"
@ -628,48 +628,48 @@
"output_type": "stream",
"text": [
"T = 0.5\n",
"\tequilibrating took 2.6317245960235596 seconds\n",
"\tmeasuring took 13.053837060928345 seconds\n",
"\tequilibrating took 2.632 seconds\n",
"\tmeasuring took 13.054 seconds\n",
"\n",
"T = 0.6\n",
"\tequilibrating took 2.8574910163879395 seconds\n",
"\tmeasuring took 12.967190027236938 seconds\n",
"\tequilibrating took 2.857 seconds\n",
"\tmeasuring took 12.967 seconds\n",
"\n",
"T = 0.7\n",
"\tequilibrating took 3.4188122749328613 seconds\n",
"\tmeasuring took 16.535584449768066 seconds\n",
"\tequilibrating took 3.419 seconds\n",
"\tmeasuring took 16.536 seconds\n",
"\n",
"T = 0.8\n",
"\tequilibrating took 3.129852294921875 seconds\n",
"\tmeasuring took 14.666396617889404 seconds\n",
"\tequilibrating took 3.130 seconds\n",
"\tmeasuring took 14.666 seconds\n",
"\n",
"T = 0.9\n",
"\tequilibrating took 2.749675750732422 seconds\n",
"\tmeasuring took 12.164067506790161 seconds\n",
"\tequilibrating took 2.750 seconds\n",
"\tmeasuring took 12.164 seconds\n",
"\n",
"T = 1.0\n",
"\tequilibrating took 2.770905017852783 seconds\n",
"\tmeasuring took 11.673817873001099 seconds\n",
"\tequilibrating took 2.771 seconds\n",
"\tmeasuring took 11.674 seconds\n",
"\n",
"T = 1.1\n",
"\tequilibrating took 2.59846830368042 seconds\n",
"\tmeasuring took 9.312909126281738 seconds\n",
"\tequilibrating took 2.598 seconds\n",
"\tmeasuring took 9.313 seconds\n",
"\n",
"T = 1.2000000000000002\n",
"\tequilibrating took 2.9586286544799805 seconds\n",
"\tmeasuring took200] 10.83272385597229 seconds\n",
"T = 1.2\n",
"\tequilibrating took 2.959 seconds\n",
"\tmeasuring took 10.833 seconds\n",
"\n",
"T = 1.3\n",
"\tequilibrating took 2.4720122814178467 seconds\n",
"\tmeasuring took 9.212384223937988 seconds\n",
"\tequilibrating took 2.472 seconds\n",
"\tmeasuring took 9.212 seconds\n",
"\n",
"T = 1.4\n",
"\tequilibrating took 3.3535523414611816 seconds\n",
"\tmeasuring took 10.767858028411865 seconds\n",
"\tequilibrating took 3.354 seconds\n",
"\tmeasuring took 10.768 seconds\n",
"\n",
"T = 1.5\n",
"\tequilibrating took 3.0648155212402344 seconds\n",
"\tmeasuring took 9.897510051727295 seconds\n",
"\tequilibrating took 3.065 seconds\n",
"\tmeasuring took 9.898 seconds\n",
"\n"
]
}
@ -686,7 +686,7 @@
" \n",
" for idx, T in enumerate(temperatures):\n",
" toc()\n",
" print(\"T =\", T)\n",
" print(\"T = {:.1f}\".format(T))\n",
" beta = 1/T\n",
" # We let the sweep size depend on the width and the average cluster size\n",
" # from before:\n",
@ -696,7 +696,7 @@
" for j in range(equil_sweeps*sweep_size):\n",
" xy_cluster_move(state,beta)\n",
" print(\"\\tequilibrating... [{}/{}]\".format(j, equil_sweeps*sweep_size), end='\\r')\n",
" print(\"\\tequilibrating took\", toc(), \" seconds\")\n",
" print(\"\\tequilibrating took {:2.3f} seconds\".format(toc()))\n",
" \n",
" # Measure\n",
" for j in range(measurements):\n",
@ -708,7 +708,7 @@
" # TODO: Skip sweeps between measurements for last measurement in set.\n",
" for _ in range(measure_sweeps*sweep_size):\n",
" xy_cluster_move(state,beta)\n",
" print(\"\\tmeasuring took\", toc(), \" seconds\")\n",
" print(\"\\tmeasuring took {:2.3f} seconds\".format(toc()))\n",
" print()\n",
" \n",
" f.create_dataset(\"square-magn\",data=square_magn)"
@ -844,37 +844,37 @@
"output_type": "stream",
"text": [
"T = 0.5\n",
"\tequilibrating took 5.539074659347534 seconds\n",
"\tequilibrating took 5.540 seconds\n",
"\n",
"T = 0.6\n",
"\tequilibrating took 5.275792598724365 seconds\n",
"\tequilibrating took 5.276 seconds\n",
"\n",
"T = 0.7\n",
"\tequilibrating took 6.957661867141724 seconds\n",
"\tequilibrating took 6.958 seconds\n",
"\n",
"T = 0.8\n",
"\tequilibrating took 6.382277250289917 seconds\n",
"\tequilibrating took 6.382 seconds\n",
"\n",
"T = 0.9\n",
"\tequilibrating took 5.454374074935913 seconds\n",
"\tequilibrating took 5.454 seconds\n",
"\n",
"T = 1.0\n",
"\tequilibrating took 5.399614572525024 seconds\n",
"\tequilibrating took 5.400 seconds\n",
"\n",
"T = 1.1\n",
"\tequilibrating took 4.563677787780762 seconds\n",
"\tequilibrating took 4.564 seconds\n",
"\n",
"T = 1.2000000000000002\n",
"\tequilibrating took 5.712708473205566 seconds\n",
"T = 1.2\n",
"\tequilibrating took 5.713 seconds\n",
"\n",
"T = 1.3\n",
"\tequilibrating took 5.183827877044678 seconds\n",
"\tequilibrating took 5.184 seconds\n",
"\n",
"T = 1.4\n",
"\tequilibrating took 6.481664180755615 seconds\n",
"\tequilibrating took 6.482 seconds\n",
"\n",
"T = 1.5\n",
"\tequilibrating took 6.137166976928711 seconds\n",
"\tequilibrating took 6.137 seconds\n",
"\n"
]
}
@ -889,7 +889,7 @@
" states = np.zeros(temperatures.shape + state.shape)\n",
" for idx, T in enumerate(temperatures):\n",
" toc()\n",
" print(\"T =\", T)\n",
" print(\"T = {:.1f}\".format(T))\n",
" beta = 1/T\n",
" sweep_size = np.ceil(width**2/f[\"cluster-size\"][idx]).astype(int)\n",
" \n",
@ -897,7 +897,7 @@
" for j in range(equil_sweeps*sweep_size):\n",
" xy_cluster_move(state,beta)\n",
" print(\"\\tequilibrating... [{}/{}]\".format(j, equil_sweeps*sweep_size), end='\\r')\n",
" print(\"\\tequilibrating took\", toc(), \" seconds\")\n",
" print(\"\\tequilibrating took {:2.3f} seconds\".format(toc()))\n",
" states[idx] = state.copy()\n",
" print()\n",
" \n",
@ -985,6 +985,14 @@
" plt.tight_layout()\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4b31ffe5",
"metadata": {},
"source": [
"The Kosterlitz-Thouless transition is vaguely visible. For $T = 1.0$ and lower, vortices and anti-vortices can be recognized. Above this temperature, this structure vanishes."
]
}
],
"metadata": {