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100 views

Is it possible to find the ground state of generalized Ising models?

Is there a general solver (or a theoretical algorithm) for obtaining the ground state configuration of the extended Ising model, which involves an arbitrary lattice, arbitrary coordination number ...
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1answer
411 views

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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1answer
124 views

Infinite-range 1D Ising model

The Hamiltonian for this system is given by \begin{equation} \mathcal{H} \{S\} = -H\sum_i S_i - \frac{J_0}{2} \sum_{ij} S_i S_j, \end{equation} where $H$ is the external magnetic field and there is no ...
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2answers
393 views

1 dimensional Ising model

How to solve the Ising model in 1D by low temperature, and high temperature expansion, and by change of variable method? Can you please give me some reference links?
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1answer
196 views

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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0answers
40 views

Ising model. What is large fluctuations of magnetization?

My background is in mathematics. I have studied the Ising model in $\mathbb{Z}^2$. The main model of statistical mechanics. Yesterday, I was reading the preliminary notes of the book Statistical ...
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0answers
35 views

Filling ising model with basis

This questions involves how to fill a lattice with ordered basis: Is there some established mathematical approach in filling a physical lattice with some colored basis (black and white here)? For ...
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0answers
52 views

Formula for the energy per site in the triangular Ising model

I'd like to check the correctness of a simulation I ran on the Ising model on a triangular by verifying if I get the good value of the mean energy per site. I found a formula giving it for high ...
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1answer
81 views

detailed balance in the context of the ising model

I am having a very basic problem understanding the idea of detailed balance, particularly in the context of the Ising model. Most references I have found contain the following phrase: "In ...
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0answers
425 views

Is this a known entropy formula?

While playing around with a variant of the one-dimensional Ising model with periodic boundary conditions I came up with a formula, let's call it $F$, whose form looks suspiciously like an entropy ...
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1answer
131 views

Physical origins of the Heisenberg model of ferromagnetism

I am trying to understand physical intuition behind the Ising and Heisenberg models (thus I am not sure if my question is appropriate for this mostly mathematical site). I will concentrate of the ...
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1answer
71 views

what's the world record in finding the ground state of the 3D Ising model

Finding the ground state of the 3D ising model (with no magnetization) is known to be NP-complete. Just wondering what is the biggest size cubic lattice someone has found the ground state of for this ...
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1answer
238 views

Acceptance probability 2D Ising Model

Disclaimer: I just found a possible solution - eventhough i don't really understand, whats wrong with my prior approach. Edit: I just tried to calculate it from scratch and found the following: $E ...
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2answers
79 views

How to calculate critical temperature of the Ising model?

Can someone name a paper or book which calculates the critical temperature of the Ising model from scratch? It might be a book and should contain the necessary prerequisites. I have had a basic course ...
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1answer
59 views

How to calculate the exchange constant of the Ising model?

The Ising model is a mathematical model of ferro-magnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic spins that can be in one ...
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1answer
61 views

Force from solenoid

I'd like to approximate the force from a solenoid, or at the very least find a formula which is proportional to the force so that I can experimentally find the constant for my particular case. ...
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0answers
44 views

Find the lowest excitation of a given Hamiltonian

Is there a standard way to find the lowest excitation energy of given Hamiltonian without knowing the eigenstates? In particular I have the find the lowest excitations of an 1D Ising Hamiltonian in 1D ...
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0answers
57 views

Simulating Quantum Annealing of the Ising model on classical hardware

I would like to simulate Quantum Annealing of a 2D square lattice Ising model on a classical computer. There are many Monte Carlo based simulators on the web. However, from my very limited ...
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0answers
43 views

XX coupling vs Heisenberg coupling

I am going through CURVATURE OF SPIN NETWORKS by Jonckheere et al. The first line of the abstract mentions XX coupling and Heisenberg coupling. What is the difference between these two couplings?
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0answers
48 views

Why isn't the 3 pts function vanishing in the Ising model by Z_2 symmetry?

The Ising model with vanishing external field possesses the $Z_2$ symmetry: $$\sigma_i \rightarrow - \sigma_i$$ implying that the 1 pt function vanishes: $$<\sigma_i> \;= 0$$ In the same ...
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0answers
139 views

2D Ising model simulations: Wolff algorithm acceptance probability with an external magnetic field

I have implemented the Wolff algorithm to simulate a 2D ferromagnet. It works by building a cluster of like spins and flipping them all at once to move quickly through phase space. In the case of no ...