# Tagged Questions

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-...

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### Some limiting cases of the Heisenberg XXZ model (2/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
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### Is there a reasonable lower bound for free energy per site of the 2D Ising model in the presence of an external field?

Given the standard Ising partition function: $$Z(\theta ,h) = \sum\limits_{\bf{x}} {\exp \left\{ {\theta \sum\limits_{(i,j) \in E} {{x_i}{x_j}} + h\sum\limits_{i \in V} {{x_i}} } \right\}},$$ is ...
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### 1D Ising Model with different boundary conditions

The Hamiltonian for one-dimensional Ising model is given by, $$\mathcal{H} = -J\sum_{<ij>} S_iS_j; \quad i,j=1,2,...,N+1$$ where $<ij>$ denotes that there is ...
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### Monte Carlo for Random Bond Ising ferromagnet

The set-up: Consider the Ising model on an $L \times L$ square lattice, where the coupling of each bond is chosen to be $+J$ (ferromagnetic) with probability $(1-p)$ and $-J$ (antiferromagnetic) with ...
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### Ising model Mean field theory and translational invariance

In the Ising model the mean value of any particular spin is: $$m = \left<s_i\right> = \frac{ \sum_{s_i}e^{-\frac{H}{T} }s_i} { \sum_{s_i} e^{-\frac{H}{T} } } .$$ I read in several ...
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### Local minima in Ising model in a Monte Carlo simulation

Is there any way to check whether in a Monte Carlo simulation using Ising model is stuck in any (false) local minima of energy or not, particularly in 3D system ?
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### Is getting the ground state of Edwards-Anderson model NP hard?

I know 1D and 2D Ising model has a general solution. And I also know getting the ground state of 2D Ising model with transverse field and 3D Ising model is NP-hard.[Onsager][Barahona] So my question ...
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### Can particle quantum spin be described with a wave function? [closed]

I'm a little confused about the idea of spin. It's been non-technically described to me as "like magnetic dipole moment", except only two possible "directions". But I feel like that's a bad analogy, ...
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### Partition function: Number of states? Doesn't add up for ising

While trying to really understanding the partition function in statistical mechanics, I tried looking at it for a 2D ising model, as that's been helpful for me for all kinds of thermodynamic values. ...
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### Some limiting cases of the Heisenberg XXZ model (1/2)

NOTE: Because this was a long question I have split it up in two different questions! For a course on quantum integrability I am reading these notes. (Franchini: Notes on Bethe Ansatz Techniques. ...
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### Infinite-range 1D Ising model

The Hamiltonian for this system is given by $$\mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j,$$ where $H$ is the external magnetic field and there is no ...
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### Ising spin vs Pauli spin matrices

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
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### If an Ising model is in contact with two thermal reservoirs, would it still experience a phase transition if one of the reservoirs is below Tc?

For example; Two reservoirs are at each end of a one dimensional or even two dimensional lattice. One of the reservoirs has the temperature T < Tc. Would the lattice site have a phase transition ...
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### Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
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### Finite temperature transverse magnetization in transverse Ising model

Consider the transverse field Ising model, with $H=-J\sum_i\left(\sigma^x_i\sigma^x_{i+1}+g\sigma^z_i\right)$ What happens to the expectation value of the magnetization $\langle\sigma_z\rangle$ at ...
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### Ising model 2-dimensional - ground state configuration

I have to prove something about the 2-dimensional ising model. The problem is the following: Prove that every nearest-neighbour and next-nearest-neighbour interaction on the square lattice \$\mathbb{Z}...