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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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Solving a system of equations involving Gaussian Integrals numerically [closed]

I wish to solve the following system of equations numerically in any software, I tried in Mathematica using the expectation functions, but I have a difficulty in understanding how to go about solving ...
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Why is the excitation energy of antiferro 1/2 spin XXZ chain associated with the $\psi_{n+2}$ and $\psi_{n-2}$

I do not understand the equation on page 5 of nagaoso's book "quantum field theory in strongly correlated electronic systems". The Hamiltonian is shown in this form $H=\frac{J_\bot}{2}\sum_{...
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Mean-field self-consistency and thermodynamic limit

Is the mean-field self-consistent-equation approach used to study, e.g., the magnetization of an Ising model able to take into account finite-size effects, or is it written, so to say, directly in the ...
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Second-order phase transition of lattice gas model

Consider the lattice gas energy: $$ H = -\epsilon \sum_{\text{n.n}}c_ic_j-\mu \sum_i c_i, $$ where $c_i$ is the occupation at $i$ and can be $0$ (empty) or $1$ (occupied). I am using the Monte Carlo ...
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Calculation of conformal dimension for Ising model in two dimensional space

Recently I was reading Ph. Di Francesco's book, "Conformal Field Theory", and in section 7.4.2 where it discussed about Ising model, conformal dimensions $(h,\bar{h})$ are deduced from ...
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References on getting the correlation function in a 3D Markov Random Field?

Does anyone know where to look to find analytical formulae for the correlation function of the Ising model on a 2D or 3D lattice (assuming toroidal or infinite is easier?), or, even better, a ...
seeker_after_truth's user avatar
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Boltzmann distribution and sigmoid

This question is probably too simple, and I am embarrassed to ask it, but I don't get what is the relation between the sigmoid functction: $f(e) = 1/(1+\exp(-e/t))$ and the Boltzmann-Gibbs ...
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(anti)commutation relation between two different fermion fields

This question is relevant to the one enter link description here As one answered in that question, different fermions species also follow anti-commutation. But why in transverse Ising field, spins on ...
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Constant in mean-field Hamiltonian

When one obtains the mean-field Hamiltonian of a (classical or quantum) spin system and then needs to find the mean-field parameters by minimizing the expectation value of the Hamiltonian, does one ...
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Correlation length in a 3d Ising slab with one dimension much smaller than the other two

Suppose I have a 3d Ising model on a cubic lattice, but one of its dimensions is much smaller than the other two. That is, I have an $L$ by $L$ by $L'$ slab with $L' << L$; in particular, $L'$ ...
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How would a system fall to the "ground state"?

This is a basic question but I struggle to grasp it really. In the Wikipedia page for Ground state, it's written According to the third law of thermodynamics, a system at absolute zero temperature ...
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Definition of quenched data set/disoprder in the context of spin glass

I cannot come across a good definition of what "quenched" means in the context of spin glass problems. I see such use as "quenched connectivity", "quenched data set", &...
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Asymptotics of 2D Ising model transfer matrix eigenvalues

The NN 2D Ising Model at inverse temperature $\beta$ and external magnetic field $h$ on an $L_1\times L_2$ sized box within $\mathbb{Z}^2$ with periodic boundary conditions $$\sigma_{L_{1}+1,x_{2}} = \...
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Parity of a 1d Ising model, and with higher order terms

I don't know if this should be asked here or in a math stack exchange, but I'll try here first. Consider the classical 1d Ising model with periodic boundary condition: \begin{equation} H_2 (\vec{\...
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Use of Binder Cumulant for Determining Critical Temperature

I am completing a computational project where I am simulating the Ising model using Monte Carlo methods, namely the Metropolis-Hastings algorithm, and the Wolff algorithm. For the Metropolis-Hastings ...
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What is parity of charge?

In the book Field Theories of Condensed Matter Physics by Fradkin: When discussing the gauge-invariant operators of $Z_2$ lattice gauge theory in Page 299, the author says Owing to the $Z_2$ symmetry,...
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Can the specific heat capacity in the Ising Model be negative?

Im working on a numerical method for the Ising model. I'm asked to calculate both the absolute magnetizetion and the specific heat capacity: $$c = \frac{\beta^2}{N} \left( \langle H^2 \rangle - \...
Gonzalo Chiva San Román's user avatar
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Why consider more than 3 dimensions in the Ising model? [duplicate]

Are there real-world physical systems to which higher dimensional ($d>3$) Ising models correspond?
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Is the Hamiltonian for the transverse field Ising model Hermitian?

I'm watching these lectures in Condensed Matter Physics. At Lec. 13, the lecturer introduces the transverse field Ising model with the Hamiltonian $$H = - J \sum_i \sigma_i^x \sigma_{i+1}^x - h \sum_i ...
Níckolas Alves's user avatar
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Phase transition in Ising Model

Consider the NN Ising model as \begin{equation} H = -J \sum_{<ij>} \sigma_{i} \sigma_{j} - h \sum_{i} \sigma_{i} \end{equation} This model has a global $\mathbb{Z_{2}}$ symmetry in the absence ...
Santanu Singh's user avatar
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Two-point-correlation in the 3D ising model

I am currently coding a 3D (Monte-Carlo) implementation of the Ising model, using the single spin-flip & Wolff algorithm. So far, I was able to calculate all the interesting observables, like $M$ ...
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Why non-extensive terms cancel out in the low temperature expansion of 2d Ising model?

I'm currently reading David Tong's lecture on Statistical Physics, and I cannot understand the logic in the following paragraph about the low temperature expansion of 2d Ising model. It can be ...
Jason Chen's user avatar
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Spontaneous magnetization in Ising model with antiferromagnetic interaction

Consider the Ising model on the square lattice with antiferromagnetic interaction between neighbouring spins. I am somewhat confused about the spontaneous magnetisation in this model at zero ...
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Why does hysteresis even exist in ferromagnet or Ising model?

I understand the math where mean field theory gives 2 (+ and -) self-consistent magnetization values for n-dimensional Ising model when the temperature is below the critical temperature. How does this ...
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Various types of correlation functions in models with random interactions

In the Ising model, spin correlations are characterized by the following correlation function $$ C_{ij} = \langle \sigma_i\sigma_j\rangle - \langle \sigma_i\rangle\langle \sigma_j\rangle $$ where $\...
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Gaussian approximation of Landau Ginzburg and Renoramalization Group

I am studing an introduction to the Renormalization Group (RG); during my course my prof. came up saying that: Landau-Ginzburg (LG) theory truncated at Gaussian order is exact at the critical point. ...
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Landau Ginzburg path integral (PI) for the Ising model at gaussian order

I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model. If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
Federico De Matteis's user avatar
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Coupling two Ising chains via an energy-energy interaction

Consider the transverse-field Ising model on a chain with periodic boundary conditions: $$ H = -\sum_{i=1}^{L} \sigma_{i}^z \sigma_{i+1}^z + h \sigma_{i}^x$$ There's a phase transition at $h=1$, which ...
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Mapping a 1D quantum Ising chain to a 2-dimensional classical Ising system

Going through Ref. 1 (I'll stick with the book's equation numbering), I'm learning about the mapping of quantum systems into classical systems. First of all let me briefly recap notation and some ...
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Ising model in three dimensions

Which book or research paper has partition function estimates of three-dimensional nearest neighbor Ising model when the external field is zero?
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Why Curie temperature is bigger for smaller lattice in 2D Ising model

Using Metropolis algorithm, Curie temperature was calculated for square lattices with different sizes 4x4, 8x8, 16x16 and 32x32. Here Curie temperature was estimated as temperature of maximum of heat ...
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Question about the duality between 2+1 d transverse-field Ising model (TFIM) and $\mathbb{Z}_2$ gauge theory

I was reading McGreevy's Lecture notes Where do QFTs come from? , and on chapter 5 he talks about a duality between the $2+1d$ transverse-field Ising model (TFIM) and the $\mathbb{Z}_2$ gauge theory, ...
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Why is my Ising Gauge Theory calculation showing magnetization?

I wrote a Mathematica code to test out the 2d Ising Gauge Theory (by computing the exact partition fucntion) on a $3\times 3$ lattice (so that there are ($4\times 3$ spins on the horizontal bonds and $...
QFTheorist's user avatar
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1 answer
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Ising model and the axiomatics of Statistical Mechanics

I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
MsTais's user avatar
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Do the random-bond Ising model correlation functions decay with the disorder strength?

I'm imagining a square lattice with Ising spins on the vertices and nearest-neighbor Ising interactions. The interaction on a given bond is ferromagnetic with probability $(1-p)$ and antiferromagnetic ...
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Where can I find the configurations corresponding to the current largest max-cut values on $G$-set graphs?

I am looking for the configurations that are behind the max-cut value in many articles about solving the Ising problem/max-cut problem on graphs, but I can't seem to find any articles with this data ...
Dániel Száraz's user avatar
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Two-dimensional Ising model for square lattices

Consider Onsager's exact solution of two-dimensional Ising model for square lattices with nearest neighbour interaction energy ‘J ‘being equal in the horizontal and vertical directions. At the ...
sangara's user avatar
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Spontaneous symmetry breaking and ergodicity

I am studying the spontaneous symmetry breaking in the mean-field Ising model and it's clear to me the necessity of taking first the thermodynamic limit and then the zero-field limit to see the phase ...
Alessandra Pìzza's user avatar
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Mean field theory for Ising model with 0,1

I'm trying to derive a mean field expression of the dependence of the mean field of a 1D Ising ring model with $\sigma_i=0,1$. What I have derived so far is: The Hamiltonian $$H=-J\sum_i\sigma_i\...
jarhead's user avatar
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1 answer
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Obtaining the Ising and XY model from the XYZ $O(3)$ model

I have the classical XYZ model Hamiltonian $\mathcal{H}$ with a magnetic field $\vec{H}$ given as \begin{equation} \mathcal{H} = -\sum_{i< j} J^x_{ij}S_i^xS_{j}^x + J^y_{ij}i^yS_{j}^y+ J^z_{ij}S_z^...
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Tunneling lowers the energy of a ground state superposition of spins up and down in the quantum Ising model

Considering an Ising model in the quantum scenario in quantum spatial dimension d=1 (that corresponds to classical D=2=d+1 dimension). Starting with the Ising model hamiltonian under the approximation ...
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2 answers
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Phase transition in Ising Model with local $\mathbb{Z}_2$ symmetry

I am studying the Ising model with a local $\mathbb{Z}_2$ gauge symmetry \begin{equation} \mathcal{H} = -\sum_{\text{plaquettes}} \sigma^z(\vec{x}, \vec{\mu})\sigma^z(\vec{x}+\vec{\mu}, \vec{\nu})\...
QFTheorist's user avatar
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1 answer
181 views

Understanding the transfer matrix for a 1D Ising Model

I apologize in advanced for how trivial this question will come to many of you. I am in fact not a Mathematician nor physicist, just a math friendly Biologist who needs to understand the transfer ...
Nick's user avatar
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Quantum Ising model phase transitions

In the classical Ising model, there are multiple ways to tackle questions regarding the existence of phase transitions. One way would be to look at spontaneous symmetry breaking of the order parameter ...
user3397129's user avatar
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Does the following generalization of the Ashkin-Teller model make sense

Ashkin-Teller (AT) model has interesting properties. I learned this from some threads here on PhysSE, particularly the recent one. In short, the AT model can be described as two layers of Ising spins. ...
Gec's user avatar
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Category related to the fusion category of 2D Ising CFT

I am very new to Category theory and would like to better understand the fusion category of 2D Ising CFT, so please forgive my imprecise wordings in this question. I understand that the Ising CFT has ...
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Binder cumulant method for non-Gaussian distributions

In the Ising model, we know that the order parameter $m$ has a Gaussian distribution for temperatures below the critical point. Measuring the exact point where this phase transition takes place was ...
SphericalApproximator's user avatar
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1 answer
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What does the mean field approximation mean in the Maier Saupe Model (and the Ising Model)?

I am trying to understand what the mean field approximation means when expressed in tensor notation for the Maier-Saupe Model of nematic liquid crystals. I am following along with Jonathan Selinger's ...
McKinley's user avatar
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Potts model Hamiltonian

I wonder about the Hmiltonian form fo the Potts model and would like to know about its matrix form using the generalized Pauli matrix. I believe it might be possible in a smiliar way applied to the ...
Alex's user avatar
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Higher-spin ising model optimization problem

Ising model is used as an Ising machine for solving the combinatorial optimization problems. The spin of the Ising machine for this application is normally 1/2. But I wonder if there is any ...
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