Questions tagged [ising-model]

The Ising model of ferromagnetism in statistical mechanics consists of discrete bimodal (+1 or −1) "spin" (moment) variables in a simple Hamiltonian interacting with their next neighbors on a lattice. The one-dimensional variant does not evince a phase transition, but the two-dimensional square-lattice one does. Use for analog and generalized discrete models on several lattices and dimensions.

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265 views

Exact Correlation Function of the 2d Ising Problem

I'm working on a variation of the Ising Model for my undergraduate thesis and I need the exact correlation function of neighbouring sites $<\sigma_{1,1}\sigma_{1,2}>$ to compare with my results. ...
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68 views

References or resource recommendation for mapping of 1D spinless Hubbard model into XXZ Heisenberg model

I read from somewhere that 1D spinless Hubbard model can be mapped onto XXZ Heisenberg model but I don't remember from where did I read this sentence. I tried googling it but couldn't find any thing ...
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Correlation functions of exactly solvable 1D quantum models

Quantum 1d spin-1/2 transverse Ising and XY models are both related to 2d classical Ising model. Are there any known simple explicit relations between correlation functions of this models? Something ...
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Can Chaos Theory be used to explain the Ising model in paramagnetic phase?

Is it possible? How can I explain the randomness of spins in the paramagnetic phase with chaos theory? In this case, is the randomness apparent? If yes, I think the temperature would be a reasonable ...
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182 views

Why entanglement entropy diverges in 2d cft?

The entanglement entropy of a region of finite length $l$ in the ground state, in 2d CFT diverges as $$S \approx \frac{c}{6} log(l)$$ (Is it c/3 or c/6 ?) Why does this diverge. In the derivation of ...
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Physical explanation of the characteristics of the order parameter of the transverse Ising Model

The Hamiltonian for transverse Ising model is $$\hat{H}=-\sum_{j=0}^{N-1}(\lambda \hat{\sigma}_j^x\hat{\sigma}_{j+1}^x+\hat{\sigma}_j^z)$$ where $\hat{\sigma}$s are Pauli matrices. This model shows ...
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378 views

Why is the critical exponent $\alpha$ negative at the Ising spin-glass transition?

The specific heat usually diverges at a phase transition - typically as a power-law, giving a critical exponent $\alpha > 0$. (Although in 2D, sometimes the divergence is only logarithmic, as with ...
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409 views

Discontinuity of free energy at phase transitions

I am learning about the two dimensional Ising model at the moment, and how it exhibits phase transitions. At the very beginning of the course we were told that: Thermodynamically, a phase ...
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1answer
480 views

What is a CFT model corresponding to a 1D transverse Ising model?

For a 1D transverse Ising model the Hamiltonian can be expressed as $$H = -J \sum_{i} S_{i}^{x}S_{i+1}^{x} - h \sum_{i} S_{i}^{z}$$ According to my understanding this undergoes a 2nd order phase ...
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How to derive ensemble average from partition function in lattice system? [closed]

I am considering a lattice model with $N$ sites. Each site is assigned with three possible spins. The number of these three possible spins are $N_1$, $N_2$ and $N_3$. So $N=N_1+N_2+N_3$. If I can ...
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Machine learning and Condensed Matter Physics [closed]

What is the state of art of the use of Machine Learning algorithms in Condensed Matter Physics and Phase transitioning? Is there any promising result that lead us to think this is a good way to pursue?...
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Theoretical prediction for absolute magnetization in 1D Ising model of a ferromagnet

In the 2D Ising model of a ferromagnet, Onsager predicts the absolute magnetization as a function of (unitless) temperature as $$|M_{2D}(T)|=\left(1-\sinh\left(\frac{\ln\left(1+\sqrt{2}\right)}{T}\...
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Can ferromagnetism be described by classical physics?

It may sound as a trivial question, but I am very confused about the origin of ferromagnetism. According to Bohr–van Leeuwen theorem, ferromagnetism cannot be predicted by classical physics. Therefore ...
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New to ising model, can't find answer to simple energy calculation

I'm trying to see why we get this energy config here As far as I understood, up/down or down/up contributes +, and same direction, ie up up or down down negative. So it should be all negative on the ...
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Analytical solution to 1D transverse Ising model

There has been a lot of work on the transverse Ising model, but when even limited to the 1D case, Monte Carlo simulations or Mean-field theory seem to have been the go-to approaches. So I wonder, has ...
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CFT with defect: Real OPE coefficients in the bulk-defect expansion?

I am studying the article by Gaiotto, Mazac and Paulos from 2013 https://arxiv.org/pdf/1310.5078v2.pdf , and I am wondering whether the OPE coefficients in the bulk-defect expansion (2.6) are real-...
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Magnetic susceptibility in zero external field?

I want to know why the magnetic susceptibility in zero external field is : (the fluctuations in magnetization) $$ \chi = \frac{1}{k_bT} \left( \langle M^2 \rangle - \langle M \rangle^2 \right)$$ ...
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357 views

Equivalence between spin 1 Ising model and 3 Potts q state model [closed]

How can I show that the spin 1 Ising model has the same symmetry as the 3 state Potts model? I want to show that on the square lattice the spin-1 Ising model, described by the Hamiltonian $H_1$, $$ ...
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Writing the mean-field Hamiltonian of the 1d Ising model including nearest and next-nearest neighbour interactions [closed]

for an exercise I have to consider the 1d Ising model with a Hamiltonian of the form H = $-J_1 \sum_{i-1}^{N}S_{i}S_{i+1} - J_{2}\sum_{i=1}^{N}S_{i}S_{i+2}$. We assume the system has periodic ...
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Equivalence between Ising model and lattice gas model [closed]

The Ising Hamiltonian is $$ H=-J \sum_{i=1}^N \sigma_i \sigma_{i+1} - H \sum_{i=1}^N \sigma_i $$ How I can show the lattice gas model Hamiltonian is equivalent to that of the Ising model?
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Transverse Ising model with longitudinal field at finite T: magnetisation, susceptibility,

In a Ising model with transversal and longitudinal fields $$ H = B_x \sum_i S_x^{(i)} + B_z \sum_i S_z^{(i)} + J \sum_{\langle i,j\rangle} S_z^{(i)}S_z^{(j)} $$ if $B_z=0$, the magnetisation $M$ and ...
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115 views

Topological Quantum Computation Resources Prerequisite

I am about to start my BSc Theoretical Physics project on Topological Quantum Computation. I have studied the basics of quantum mechanics, condensed matter phys, statistical mechanics. Are there any ...
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Mean magnetization of the Ising model at the first-order transition line

Below the Currie temperature, the Ising model shows first-order phase transition if we consider the external field as the control parameter. The order parameter jumps from e.g., $-m_0$ to $m_0$. The ...
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How do WZW coset models contain perturbations?

I've been studying the coset construction. As far as I understand it, the Sugawara energy momentum tensor is a way of embedding the virasoro algebra inside the Lie algebra of your original WZW model. ...
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Peierl's Proof on Spontaneous Magnetization

How to modify Peierls proof to show that, for the Ising model on the hexagonal lattice with nearest neighbor ferromagnetic coupling $J$, at low temperatures there is a spontaneous magnetization?
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Ground State Entropy of a Ferromagnet and Antiferromagnet

Consider the ground state of a 1D Ising model. In the ferromagnetic case, if we are to have magnetisation along the z axis, then there is one possible microstate, with all spins aligned along z. ...
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Estimating the Free Energy of a Kink

In statistical mechanics, people often estimate whether or not a certain feature will occur by estimating the feature's free energy. For example, in the 1D Ising model, they want to estimate the ...
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257 views

Virasoro primary for 2D Ising model at critical point

It is well known that 2D Ising model at critical point can be described by a 2D CFT. The CFT is identical to free Majorana fermions. It has three primary operators namely The identity. The Ising ...
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Maximum value of the microcanonical distribution for the finite 2D Ising model

Here's an interesting combinatorial problem relating to the two-dimensional N x N Ising model, whose energy is given by $$E=-\sum_{(i,j)pairs} Js_is_j, $$where the value of nearest-neighbor cells are $...
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Does Heisenberg ferromagnet has inifinite number of phases below the critical temperature?

This is an upshot of the question here. The up-aligned and the down-aligned spin configurations are assumed to be two distinct phases in case of an Ising ferromagnet. But for Heisenberg ferromagnet, ...
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802 views

Are the first order phase transitions always associated with a latent heat?

Is the first order ferromagnetic transition below the critical temperature associated with latent heat? For example, the transition of ferromagnetic configuration with all its spins aligned up to a ...
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1answer
153 views

Are all correlation functions in a CFT non-zero?

I am particulary interested in the Ising CFT. Is it clear/true that for any field $\phi$ and a large enough number $r \in \mathbb R^+$, we have that $\langle \phi(x) \phi(y) \rangle \neq 0$ if $|x-y| &...
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Confusion on the Origin of Summation Approximations in the Mean Field Ising Model

Much of the literature on the mean field approximation to the Hamiltonian of the Ising Model seems to take the the treatment of the summations in the model as a trivial step to the full mean field ...
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Ising anyon topological order and its edge $c=1/2$ CFT

We know that conformal field theories are closely related to two-dimensional topological orders via edge-boundary correspondence. An Ising topological order can be obtained by gauging the fermion ...
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1answer
977 views

Antiferromagnetic and Ferromagnetic Ising Model on triangular lattice

Recently I heard a report about the antiferromagnetic Ising model in triangular lattice. It's interesting and I never realized that the result in triangular lattice would be so different from square ...
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Fermionic Hamiltonian: questions on Bogoliubov transformation and Hermiticity

In section 2.A.2 of Quantum Ising Phases and Transition in Transverse Ising Models by Suzuki, et. al. the authors give the following in their derivation of the Bogoliubov transformation for a ...
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What does it mean to Taylor expand free energy density “in gradients”?

I am self-studying Statistical Mechanics from J. Sethna's book Entropy, Order parameters, complexity. In one of the exercises (page 206), the Landau theory for the Ising Model is derived. Starting ...
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521 views

Partition function for 1D XY model [closed]

The Hamiltonian for 1D XY Model for $N$ Ising spins is written as, $$H=\sum_{i=1}^{N} \vec{S_i} . \vec{S_{i+1}} =\sum_{i=1}^{N} cos(\theta_i-\theta_{i+1})$$ Here we will implement periodic boundary ...
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1answer
128 views

Lee-Yang zeros, how to define activity

I'm studying Lee-Yang theorem following Volume I, Section 3.2 of Itzykson and Drouffe famous book. In doing so, I've stumbled upon a dilemma that - while almost ...
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Naive question about the physical dynamics for classical Ising model

Suppose we have a 2D Ising model in physical world, at finite temperature, the system have to obey the Boltzmann distribution: $$P(\{s_i\})=\frac{1}{Z}\exp^{-\beta E(\{s_i\})}$$ where $Z$ is the ...
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1answer
203 views

1D Ising model as indpendent coin tosses : Partition function calculation

My query refers to the Wikipedia article on the one-dimensional Ising model, namely the section "Comments", immediately after "Ising's exact solution". An Ising model with Hamiltonian $$ H = -J \sum \...
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397 views

Critical slowing down in Monte-Carlo algorithm for classical 2D Ising Model

Why do local updates (i.e. local spin flips) near the phase transition in MC algorithm for classical 2D Ising model are said to be not "effective" and lead to incorrect critical indices? I understand ...
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Ising model density of states

1D Ising model: exact result In the 1D Ising model with fixed $J_{ij} = J$, without magnetic field, the density of states (dos) can be calculated exactly. There is a caveat in the case of periodic ...
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The need for the Ising model in Mean field theory?

Consider the Heisenberg Hamiltonian: $$\newcommand{\p}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\f}[2]{\frac{ #1}{ #2}} \newcommand{\l}[0]{\left(} \newcommand{\r}[0]{\right)} \newcommand{\mean}[...
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Exact solution of the 2D Ising model in an external magnetic field?

The 2D Ising model is a thoroughly studied model. One of the remarkable features of the model is that it predicts a hysteresis. However, I cannot seem to find the appropriate literature on this ...
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85 views

About three conserved quantities in a 1d spin model

In 1d spin model with periodic boundary condition with N sites, each site has a spin. Now I have a Hamiltonian for this model, and I want to restrict this Hamiltonian to the sector with quasimomentum $...
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1answer
96 views

Finding conservation quantities in Ising Hamiltonian

I have a Ising model, for example: $$H =\sum_{<ij>} J(\sigma_i^x\sigma_j^x+\sigma_i^y\sigma_j^y)+h\sigma_i^z\sigma_j^z$$ Assuming periodic boundary condition, and the number of site is ...
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Critical exponents from Ising free energy at zero magnetic field?

Consider the free energy of an Ising model $f(J,h,T)$, where $J$ is the coupling between neighboring sites, $h$ is the magnitude of a homogeneous external magnetic field and $T$ is the temperature. ...
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790 views

Is the Ising CFT different from the Majorana CFT?

If by 'Ising CFT' I mean the conformal field theory describing the critical quantum Ising chain $ H = \sum_n \left( \sigma^z_n - \sigma^x_n \sigma^x_{n+1} \right)$ and by 'Majorana CFT' I mean the ...
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Transfer Matrix formalism

I am trying to apply the transfer matrix formalism to an Ising model problem, and am having some difficulties deriving the correct matrix to use. The problem is as follows. There is an infinite chain ...