Institut für Theoretische Physik Universität zu Köln
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Prof. Dr. Simon Trebst Jan Attig
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Statistische Physik
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Übungsblatt 12
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Wintersemester 2020/21
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"**Website** [http://www.thp.uni-koeln.de/trebst/Lectures/2020-StatPhys.shtml](http://www.thp.uni-koeln.de/trebst/Lectures/2020-StatPhys.shtml)\n",
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"**Name**: Bitte geben Sie ihren Namen an\n",
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"**Matrikelnummer**: Bitte geben Sie ihre Matrikelnummer an"
]
},
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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Der Ising Ferromagnet\n",
"\n",
"Nachdem wir in der letzten Woche mit dem Ising Paramagneten ein erstes klassisches Spin-Modell aus nicht-wechselwirkenden Ising-Spins in einem Magnetfeld diskutiert haben, möchten wir nun den Effekt von paarweisen **Wechselwirkungen** zwischen den Ising Spins untersuchen. Der Modell-Hamiltonian wird dazu wie folgt erweitert:\n",
"\n",
"\\begin{equation}\n",
" \\mathcal{H} = -J \\sum_{\\langle \\alpha,\\beta \\rangle} \\sigma_\\alpha \\sigma_\\beta + \\sum_{\\alpha} -h \\sigma_\\alpha \\,.\n",
"\\end{equation}\n",
"\n",
"Hierbei wird im zweiten Term wieder über alle Plätze eines Gitters summiert (wie etwa einem Quadratgitter in der unten stehende Abbildung). Der Index $\\alpha$ bezeichnet dabei die verschiedenen Spins und kann z.B. ausgedrückt werden durch einen Tupel an Indices für die Gitterkoordinaten: $\\alpha = (i,j)$.\n",
"Die Summe über $\\langle \\alpha \\beta \\rangle$ im ersten Termn läuft über *benachbarte* Spins $\\sigma_\\alpha$ und $\\sigma_\\beta$ im Quadratgitter (siehe Abbildung).\n",
"\n",
"![Ising_sketch.png](attachment:Ising_sketch.png)\n",
"\n",
"Wir möchten im folgenden erneut eine numerische Simulation dieses Modell-Systems aufsetzen und anhand eines Monte Carlo-Verfahrens Observablen des Systems, insbesondere die Magnetisierung und spezifische Wärme, berechnen."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Metropolis Monte Carlo\n",
"\n",
"Für die numerische Messung der Observablen haben wir Ihnen erneut den Metropolis Monte Carlo Code des Ising Paramagneten, d.h. des Systems ohne Wechselwirkungen, zur Verfügung gestellt.\n",
"\n",
"Zur Erinnerung: Der Algorithmus läuft nach folgendem grundsätzlichen Schema ab:\n",
"\n",
"1. Zuerst werden Funktionen implementiert, die Ising Spins einzeln oder als Vielteilchen-Konfiguration erzeugen und diese plotten. Damit wird im Programm die Möglichkeit geschaffen, Konfigurationen von Spins zu erzeugen und zu untersuchen.\n",
"2. Für die bestehenden Konfigurationen wird eine Energie nach oben stehendem Hamiltonian definiert. \n",
"3. Mit Hilfe der Energie lässt sich ein einzelner Metropolis-Update als Funktion definieren. Speziell werden hier die Übergangswahrscheinlichkeiten so implementiert, dass Konfigurationen gemäss der Boltzmann-Gewichte erzeugt werden wenn wir eine längere Markov-Kette erzeugen (siehe Computer-Physik).\n",
"4. Als letzter Schritt folgt die Messung thermodynamischer Observablen entlang dieser Markov-Kette (also nach jedem Metropolis-Update).\n",
"\n",
"Führen Sie für zuerst die Implementation der Funktionen nachfolgende Zellen aus.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function get_Ising_spin()\n",
" # Pruefe ob Zufallszahl zwischen 0 und 1 groesser als 0.5\n",
" if rand() > 0.5\n",
" return +1\n",
" else\n",
" return -1\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function get_Ising_spins(Lx, Ly)\n",
" # neues Array fuer die Ising Spins\n",
" spins = zeros(Int64, Lx, Ly)\n",
" # Alle Spins im Array auf zufaeelige Spins setzen\n",
" for i in 1:Lx\n",
" for j in 1:Ly\n",
" spins[i,j] = get_Ising_spin()\n",
" end\n",
" end\n",
" # Spins zurueckgeben\n",
" return spins\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Importieren von PyPlot\n",
"using PyPlot\n",
"pygui(false)\n",
"\n",
"function plot_Ising_spins(spins)\n",
" # neue Figur anlegen\n",
" figure() \n",
" # Die Spins plotten mittels imshow (in Schwarz-Weiss)\n",
" imshow(spins', cmap=\"gray\", origin=\"lower\", interpolation=\"None\", vmin=-1, vmax=1)\n",
" # keine Axenbeschriftung\n",
" axis(\"off\")\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function get_energy_of_spin(spin_array, J,h, i,j)\n",
" # HIER MUSS ERGAENZT WERDEN\n",
" return -h*spin_array[i,j]\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function get_energy(spin_array, J,h)\n",
" energy = 0.0\n",
" for i in 1:size(spin_array)[1]\n",
" for j in 1:size(spin_array)[2]\n",
" energy += get_energy_of_spin(spin_array, J,h, i,j)\n",
" end\n",
" end\n",
" return energy\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function update_SSF!(spin_array, J,h, T)\n",
" # Update vorschlagen\n",
" i = rand(1:size(spin_array)[1])\n",
" j = rand(1:size(spin_array)[2])\n",
" # dE ausrechnen\n",
" # HIER MUSS ERGAENZT WERDEN\n",
" dE = 2*h*spin_array[i,j]\n",
" # Akzeptieren Ja / Nein\n",
" if rand() < exp(-dE / T)\n",
" # JA\n",
" spin_array[i,j] *= -1\n",
" else\n",
" # NEIN\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"function sweep_SSF!(spin_array, J,h, T)\n",
" # Anzahl spins an Update vorschlagen\n",
" for u in 1:size(spin_array)[1]*size(spin_array)[2]\n",
" update_SSF!(spin_array, J,h, T)\n",
" end\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# Magnetisierung definieren\n",
"function get_magnetization(spin_array)\n",
" return sum(spin_array)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# a) Wechselwirkungen und Energie eines Spins\n",
"\n",
"Durch das Hinzufügen von Wechselwirkungen verändern wir die Energie, die ein einzelner Spin besitzt. Machen Sie sich klar, welche Energie jetzt einem einzelnen Spin zugeordnet wird und implementieren Sie diese Änderung in die Funktionen `get_energy_of_spin` und `update_SSF!` an den gekennzeichneten Stellen."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# b) Magnetisierungskurven\n",
"\n",
"Plotten Sie, wie in der vergangenen Woche, Magnetisierungskurven als Funktion des äußeren Magnetfelds für verschiedene Temperaturen. Vergleichen Sie dabei insbesondere das Verhalten des Paramagneten ($J=0$) mit dem eines wechselwirkenden Systems ($J=1$) für verschiedene Temperaturen ($T=0.1, 1, 2, 5$).\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# c) Spezifische Wärmekapazität\n",
"\n",
"Um das unterschiedliche Verhalten bei verschwindendem Magnetfeld und kleinen Temperaturen weiter zu verstehen, betrachten wir im folgenden die thermodynamischen Signaturen verschiedener Größen für den Fall *ohne* äußeres Magnetfeld. \n",
"\n",
"Als erstes betrachten wir dazu die spezifische Wärmekapazität, die definiert ist als\n",
"\n",
"\\begin{equation}\n",
" C_V = \\frac{1}{N}\\left.\\frac{\\partial \\langle E \\rangle}{\\partial T}\\right|_V\n",
"\\end{equation}\n",
"\n",
"Sie kann deswegen entweder als Ableitung der bereits berechneten Kurve $E$ vs. $T$ ermittelt werden, oder — noch eleganter — über die Mittelwerte von $E$ und $E^2$ durch\n",
"\n",
"\\begin{equation}\n",
" C_V = \\frac{1}{T^2 N} \\left(\\langle E^2 \\rangle - \\langle E \\rangle^2 \\right)\n",
"\\end{equation}\n",
"\n",
"Leiten Sie diesen Ausdruck her und berechnen Sie die Wärmekapazität mit Hilfe Ihrer Monte Carlo Simulation in Abhängigkeit der Temperatur für den Fall $J=1$ und $h=0$.\n",
"\n",
"*Hinweis (1): Um einen bestimmten Bereich der Kurve besser auflösen zu können, können Sie die Temperaturpunkte aus der nachfolgenden Zelle benutzen.*\n",
"\n",
"*Hinweis (2): Damit Sie glatte Kurven berechnen, sollten Sie eine angemessene Anzahl an Thermalisierungs- und Mess-Sweeps durchführen, z.B. 10000 Sweeps für die Thermalisierung und 100000 für die Messung.*"
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"T_vals = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.05, 2.1, 2.15, 2.2, 2.25, 2.3, 2.35, 2.4, 2.45, 2.5, 2.55, 2.6, 2.65, 2.7, 2.75, 2.8, 2.85, 2.9, 2.95, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.2, 6.4, 6.6, 6.8, 7.0, 7.2, 7.4, 7.6, 7.8, 8.0];"
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"# d) Ordnungsparameter: Magnetisierung\n",
"\n",
"Plotten Sie jetzt den Ordnungsparameter des Systems, die Magnetisierung pro Spin, als Funktion der Temperatur bei äußerem Feld $h=0$ und beschreiben Sie das qualtiative Verhalten.\n",
"\n",
"Untersuchen Sie danach das Verhalten für ein kleines externes Magnetfeld $h=0.1$. Was hat sich verändert und warum?"
]
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"# e) Magnetische Susceptibilität\n",
"\n",
"Analog zur Berechnung der spezifischen Wärmekapazität aus Variationen der Energie lässt sich auch die magnetische Susceptibilität\n",
"\n",
"\\begin{equation}\n",
" \\chi = \\frac{1}{N}\\left.\\frac{\\partial \\langle M \\rangle}{\\partial h}\\right|_T\n",
"\\end{equation}\n",
"\n",
"aus Variationen der Magnetisierung berechnen:\n",
"\n",
"\\begin{equation}\n",
" \\chi = \\frac{1}{NT} \\left(\\langle M^2 \\rangle - \\langle M \\rangle^2 \\right)\n",
"\\end{equation}\n",
"\n",
"Leiten Sie auch diesen Ausdruck her und berechnen Sie die Susceptibilität mit Hilfe Ihrer Monte Carlo Simulation in Abhängigkeit der Temperatur für den Fall $J=1$ und $h=0$."
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