Tagged Questions

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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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NP-completeness of non-planar Ising model versus polynomial time eigenvalue algorithms

From the papers by Barahona and Istrail I understand that a combinatorial approach is followed to prove the NP-completeness of non-planar Ising models. Basic idea is non-planarity here. On the other ...
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Ising Hamiltonian for relativistic particles

An Ising system is described by the simple Hamiltonian: $$H = \sum\limits_{i} c_{1i} x_{i} + \sum\limits_{i,j} c_{2ij} x_i x_j \,\,\,\,\,\,\,\,\,\,(1)$$ Here the $x_i$ are spins (+1 or -1 in units ...
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Question about the derivation of an equation in full replica symmetry breaking solution

Using replica method and saddle point method, the free energy of a magnetic system can be expressed as -\beta[f]=\lim_{n\to0}\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta ...
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Partition function of bosons vs fermions

I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively. What's the difference between ...
Highly related to A reading list to build up to the spin statistics theorem I see 2 parts to the spin statistics theorem: (spin $n$ or $n+\frac{1}{2}$) step 1 given that a spin is integral or ...