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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How to compute correlation function and length for a given lattice configuration?

Focusing on the Ising model, for a given lattice configuration of up and down spins (say square or triangular lattice), and a given interaction type (ferromagnetic or antiferro), how can one compute ...
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Why do fermions anti-commute in Ising model?

In my course fermions are given like a product of spin and (dual to spin) disorder parameter in 2D Ising square lattice. Then, using the properties of disorder parameter I can prove that fermions ...
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How to get mass near the critical point for 2D Ising model on square lattice for fermions?

Let's assume that we have 2D square lattice with spins $\sigma=\pm 1$ and equal vertical and horisontal energy coefficients K: $$E_{interaction}=e^{K\sigma_i\cdot\sigma_j}$$ where $\sigma_i,\sigma_i$ ...
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How do spin operators work? [closed]

I am currently studying statistics and 2D Ising models and noticed in my lecturer's notes the operators, acting in the spin space The text says that this is identity $2^N\times 2^N$ matrix. I don't ...
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How does the value $k$ work in MCMC algorithm in the case of Ising model?

Here they say that $k$ is Boltzmann's constant. However, here they are saying that $k$ is a variable Can anyone explain what the catch is here?
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What is the fundamental difference between the Ising and Potts models?

What I understand is that the only difference between the Ising and Potts models is that Ising has two types of spins, and Potts has n types of spins. However, I am wondering if the Hamiltonian (...
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How to formulate the braiding of instanton?

I'm reading the paper https://arxiv.org/abs/2108.08835, after imposing the $\mathbb{Z}_2$ on-site symmetry, in the $J=0$ symmetric phase of the 1d Ising chain, the topological sectors of operators ...
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What is a "transient state" and "transition state" in Ising model?

I was analyzing this source code of the Ising model. I found the term "transient state". I also found the term in this text: There are two absorbing states in this Markov chain because once ...
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Eigenvector of ground state (GS) of spins and fermions

I'm working with the hamiltonian of XX model on a spin basis and in a fermionic basis. I have the following problem to solve: In the ground state, the number of spins up (and by convention, fermions) ...
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Magnetization in the quantum Ising model

In the quantum Ising model $$\hat H=-J\sum_{j=1}^n \hat\sigma_j^z\hat\sigma_{j+1}^z-g\sum_{j=1}^n\hat\sigma_x $$ there is a quantity of interest, namely the average magnetization along the $z$-axis $\...
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Action of Pauli matrices after change of basis

Let $X$, $Y$, and $Z$ be the Pauli matrices represented by $$X=\begin{pmatrix}0&1 \\ 1 & 0\end{pmatrix}, \quad Y=\begin{pmatrix}0&-i \\ i & 0\end{pmatrix}, \quad Z=\begin{pmatrix}1&...
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Signature of quantum phase transition in sudden quench

Let's say I have a system which undergoes a phase transition, if a parameter $g$ of system is greater than some $g_{c}$. Suppose if the system is in normal phase $(g < g_{c})$ and I suddenly ...
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How do I initialize the lattice/grid in a Potts Model?

I am studying the following: Cellular Potts Model Tutorial However, either this doesn't say anything about the grid/lattice initialization, or I failed to find any indication. How do I initialize ...
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MC condition in Cellular Potts Model

In the following discussion, Introduction to the CPM I haven't understood the following MC condition: Note the "try" in the previous sentence; this so-called "copy attempt" only ...
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How shift the system Hamiltonian change the interaction term?

I'm reading this paper about a model of a qubit coupled to an Ising spin bath. The interaction between the system qubit and the bath is described by the Ising Hamiltonian: $$H_{I}^{\prime}=\alpha \...
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Problem in code for Monte Carlo method for frustrated Ising model

I'm studying Monte Carlo method (it's related to my school project). The code I'm using I got from a paper by Jacques Kotze (https://arxiv.org/abs/0803.0217). In his paper, he uses the Monte Carlo ...
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Computation of two-site entanglement entropy of the critical transverse-field Ising chain

The paper Osborne and Nielsen, Phys. Rev. A 66, 032110 gives an exact solution for the two-site reduced density matrix for the transverse-field Ising model with periodic boundary conditions (Eq. 26): $...
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Entanglement entropy of the infinite transverse field Ising chain at the critical point

Consider the $1$D transverse-field Ising model, $$H = -\sum_i \sigma_i^z \sigma_{i+1}^z-h\sum_i \sigma_{i}^x$$ at the critical point $h=1$ with periodic boundary conditions. Question: What is the (von ...
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Reference on Curie-Weiss model

I am looking for a reference on the Curie-Weiss model and mean-field approximation. Model. Consider the Curie-Weiss model with the following Hamiltonian: \begin{align*} H = - \frac{J}{2N} \sum_{i \neq ...
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Qubit Resource Estimates for 2D Ising Model

I recently came across this paper where the 1d Transverse Field Ising Model (TFIM) with $n$ spins was simulated on a quantum computer. The estimated resources were $n^2$ for the number of gates and ...
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Flipping multiple spins in Ising model

I am currently working on the Ising model in 2D using the Monte Carlo simulation. What I face is that sampling physical properties such as susceptibility, magnetization, and specific heat are not ...
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Why is the free energy unitless when taking the thermodynamic limit?

Why is the (Helmhotz) free energy unitless when taking the thermodynamic limit? Given the partition function $Z$ of a (finite size) system, the free energy is given by $F =-kT \log[Z]$, where $k$ is ...
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How was the minimal model with a boundary related to the D brane?

Quote my advisor: The D brane was the boundary of the CFT However, in the development of the rational CFT, such as the minimal model, the D brane was not realized. Thus, when the boundary CFT was ...
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Ising model correlation function in the high temperature limit

I'm reading the book 'Gauge Fields and Strings' by A. Polyakov and I don't understand his derivation of the correlation function of the Ising model in the high temperature limit. I don't really ...
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Transfer Matrix for Ising model- Notation Issue

I having difficulties in understanding "transfer matrix" in the paper Metastability in the two-dimensional Ising model. They consider a periodic $N \times \infty$ lattice with the energy $$ ...
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Peierls's argument for the Ising model

I was reading about Peierls's argument for the Ising model at this link and got a question. The Hamiltonian is $$ H = -J \sum_{(i,j)} \sigma_i \sigma_j - \sum_i h_i \sigma_i $$ with the first ...
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Who found the Ising transition?

The famous story is that Ernst Ising studied the 1d classical stat mech model which bears his name, argued it has no phase transition, and guessed that the same would hold in all dimensions. He was ...
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How to understand the Ising model and its relation to (recurrent) neural networks

This question relates two questions I have recently asked here, about solid state physics (How will crystal orientation affect the mobility?) and neural system models (How to understand the largest ...
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Why are Eigenvectors of a 1D quantum ising hamiltonian real

I was modelling the 1D transverse quantum Ising model and made a Kronecker product loop to find the Hamiltonian of the system, for a given magnetic field configuration. Now, my question is that when I ...
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Is Bogoliubov transformation simply a basis transformation?

I encounter Bogoliubov transformation when I'm learning 1D transverse field Ising Model.But I think it's just a simple basis transformation, I don't understand why people give it a special name?
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Ising Model without periodic boundary conditions (PBC)

I try to calculate the correlation function $<\sigma_i \sigma_j>$ with the method of transfer matrices. I do understand how to use this method with PBC. But how can I do it without PBC? My ...
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Bragg-Williams microcanonical esemble

In this question Bragg-Williams theory of phase transition of the forum someone was asking for Bragg-Williams aprox. and how to calculate entropy. The answer is clear and correct, the Bragg-Williams ...
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Solving the quantum XX model using drone fermions

Suppose we wish to solve the XX model in 1D, which describes spin-$\frac{1}{2}$ particles interacting with their nearest neighbor. Assuming open boundary conditions for simplicity, the Hamiltonian ...
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Critical point in 2D Potts model and duality equation

I have to prove, considering the limits of high and low temperatures, duality equation: $$ Z=q e^{2 N K} F\left(e^{-K}\right)=q^{-N}\left(e^{K}+q-1\right)^{2 N} F\left(\frac{e^{K}-1}{e^{K}+q-1}\right) ...
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1D Ising model correlations

I am calculating different things in Ising 1D ring model using Trasfer matrix method: $$Z_{N}=\sum_{\left\{\sigma_{i}=\pm 1\right\}} \exp \left(K \sum_{i=1}^{N} \sigma_{i} \sigma_{i+1}+h \sum_{i=1}^{N}...
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Quantum partition of two integer spins

I am trying to write the partition function for a simple system made of two interacting bosons of spin $S=1$ having the interaction Hamiltonian $$ \hat{H} = \vec{S}_1 \cdot \vec{S}_2 $$ I think I ...
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Critical exponents and scaling dimension

It is often stated that the scaling exponents, e.g. $\alpha$ and $\beta$, of the critical 2D Ising model are related to the scaling dimensions $\Delta_{\sigma}$ and $\Delta_{\epsilon}$ of the ...
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How to solve this integral?

I am following some notes from a physics class on the Ising model. At some point we get to this integral \begin{equation} \frac{1}{2} \int_{\Omega_B} \frac{\text{d}^Dk}{(2\pi)^D} \ln \left[ \tau + \...
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Is the common formulation for (Ising Model) Monte Carlo simulations a bit off?

A common [Ising Model] Monte Carlo simulation repeats the following algorithm: randomly pick a [flip] event compute change in energy $\Delta E$ if new energy is lower than old energy, accept the ...
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Eigenvalue of transfer matrix using Monte Carlo in 2D Ising model

Montecarlo is an algorithm capable of numerical estimation of any quantity which can be written as the average of a state function like, for example, the magnetization or the internal energy in the 2D ...
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Mean-field theory for a heterogeneous Ising model with two types of particles

Let's say I have an Ising model, but this time with two kinds of particles, A and B. Let the spin of particle A be denoted by $\sigma ^a$, and the spin of particle B by $\sigma ^b$. Let the total ...
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Overlap of Matrix Product States (Python)

I'd like to implement the TEBD (finite, real time evolution) by hand (in python) and want to compute the overlap of a reference MPS with the time evolved MPS. I want to regard a simple Ising Chain. ...
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Entropy of a spin spontuaneous simmetry breaking?

The Shannon entropy of a probability mass function is $$H(S) = -\sum_s p(s)\log_2 p(s),$$ where the sum runs over all the configurations $s$. If a system $S$ stays half of the time in the ...
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How to take into account finite temperature in transverse Ising chain?

A similar question has already been asked here What I'm wondering is how to take into account finite temperature in the transverse Ising chain and see how that affects the magnetization. The reason ...
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Meaning of 'thermalization' in Markov Chain Monte Carlo simulations

In performing MCMC simulations, it is standard practice to 'equilibriate' or 'thermalize' the system and then discard the initial data before useful sampling is done. My question is about the concept ...
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Reference request: Kawasaki dynamics for Ising model

I want to learn more about Glauber and Kawasaki dynamics which, by my understanding, are used to model lattice spin systems for the pre-equilibrium Ising model. There seems to be quite a few ...
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Transverse field Ising model quantum phase transition

I am looking at the quantum phase transition of the transverse field Ising model. Let: \begin{equation} H = -J \sum_{x=1}^{N-1} \sigma_x^3\sigma_{x+1}^3 - B \sum_{x=1}^N \sigma_x^1 \end{equation} Once ...
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Ground state energy from Hamiltonian [closed]

It has been a long time since I did QM, and I am getting stuck at the most basic stuff. Assume I have a Hamiltonian: \begin{equation} H = \int_{-\pi}^\pi f(q) \left[\alpha^\dagger_q, \alpha_q \right]\...
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Scaling of "non-reduced" parameters in RG theory

I'm studying quantum phase transitions using the Renormalization Group (RG) method. In Continentino's book "Quantum Scaling in Many-Body Systems: An Approach to Quantum Phase Transitions" ...
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Anticommutation and Bogoliubove transformation

I am given the following transformation: \begin{equation} \begin{bmatrix} ...

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