Questions tagged [ising-model]

Question 1

I have a very basic confusion about the 2D random-bond Ising model on a square lattice with Boltzmann weight $$\omega(J_{ij},\sigma_j)=\prod_{ij}(1-p)^{\delta_{J_{ij}=1}} p^{\delta_{J_{ij}=-1}} e^{-\...

Question 2

I'm working through Chapter 14 of Mezard and Montanari's Information,Physics,and Computation ("Belief Propagation"). I'm stuck on Exercise 14.10 in Section 14.4 about the 2d Ising model. In ...

Question 3

When reading about phase transitions, one quickly encounters the Ising model and its variants (spin glass, Potts, etc.). This model is used to explain ferromagnetism in a very satisfying way. It is ...

Question 4

I'm totally new to tensor networks, and I'm currently learning on my own from papers, tutorials, and videos. Right now, I'm trying to understand how to construct a Matrix Product Operator (MPO) for a ...

Question 5

I’m working on exercise 11.6 (a) in Conformal Field Theory by Di Francesco, Mathieu & Sénéchal (the “yellow book”). The problem defines the parity operation as $$ P:\qquad \psi(z)\longrightarrow\...

Question 6

Introduction I'm studying the Ising Model described by the partition function: $$ Z = \sum_{\{s_{i}\}} \exp \bigg\{ \dfrac{1}{2} \, \vec{s} \, \mathbf{J} \, \vec{s}^{\,\scriptscriptstyle T} \bigg\} ...

Question 7

Not a physicist, apologies in case I lack rigor. Consider the following Hamiltonian: $$H=\sum_j \gamma_j\sigma^z_j\sigma^z_{j+1} + h\sum_j \sigma^x_j.$$ I am looking for a lower-bound to the spectral ...

Question 8

I am asking about the infinitely long layered Ising model with a finite number of layers. The model is assumed to be invariant under translations along the direction in which it is infinite. All ...

Question 9

Does Jordan-Wigner transformation produce the eigenvectors of Ising model? My understanding of diagonalisation for quantum mechanics is that it can help you calculate the propagator of a Hamiltonian ...

Question 10

The Wikipedia page on the critical exponents of the Ising model presents the following table: This page lists the critical exponents ($\alpha$, $\beta$, $\gamma$, ...) and their values for some ...

Question 11

The susceptibility is defined by $\chi = \partial M/ \partial H$ and for a ferromagnet above the critical temperature $T_C$, it is given by the Curie--Weiss law, $\chi \propto (T-T_C)^{-1}$. What ...

Question 12

There is quite a lot of discussion on SE about correlation functions in lattice models. So I would say that it is well known that the two-spin (two-point) correlation function has the following ...

Question 13

I'm not versed at all in high energy physics, I come from a statistical mechanics background, hence, all of what follow is far from my comfort zone. I will also talk about what is, I believe, the lore ...

Question 14

Consider the Ising model in $d$ dimensions with a random local magnetic field $H_i$: $$ \mathcal{H} = -\frac{J}{2} \sum_{\langle i, j \rangle} S_i S_j - \sum_i H_i S_i $$ where $\langle i, j \rangle$ ...

Question 15

I'm reading this article which shows the breakdown of the Mermin-Wagner theorem for a 2D system with finite size. In short, the Mermin-Wagner theorem states that no system with dimensionality d $\leq2$...

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Questions tagged [ising-model]

Phase transition for first moments in the 2D random-bond Ising model

Belief propagation equations for 2d Ising model

Do we have good general models for solid-liquid phase transitions?

How do you represent Hamiltonian in Matrix Product Operator (MPO) representation?

Parity transformation of Ising model (Di Francecso exercise)

Kronecker's Delta definition in Ginzburg-Landau Ising Model

Spectral gap lower-bound for transverse Ising model?

Is it possible to analytically continue magnetization in one-dimensional Ising models?

Does Jordan-Wigner transformation produce the eigenvectors of Ising model?

How is the general expression for critical exponents established?

Is the susceptibility of a ferromagnet defined below the critical temperature?

Can the index in the pre-exponential factor in the correlation function depend on the direction?

Coleman-Weinberg mechanism in $\phi^4$ theories in $d=4$

Clarification about random field energy in Imry-Ma argument

Why the 2D Ising model shows a phase transition while the 1D does not? [duplicate]

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