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Ising formulation of the graph isomorphism problem

Context I have been going through Ising formulations of many NP problems by Andrew Lucas. In section 9 on page 22, the author gave an Ising formulation of the graph isomorphism problem. Here I ...
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spin (+1,-1) to binary notation (0,1) for patterns in Hopfield neural network

I have a probability distribution such as: $$P(s) = \frac{(1+a)\delta(s-1)}{2} + \frac{(1-a)\delta(s+1)}{2}$$ $s$ can take two values $+1$ and $-1$ Now if I introduce the variable change $v = ...
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Generalization of a spin-glass order parameter definition

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. Equation 4 on the second page gives the definition of the spin-glass order parameter as ...
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77 views

The “replica trick” initial formula?

In Spin-glass theory for pedestrians by Castellani and Cavagna, the initial formula used to introduce the replica trick is written as: $$\overline{\log ...
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103 views

Spin Glass Prince Rupert's Drop

Spin Glass is known to converge to its ground state under Simulated Annealing. The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
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What is the difference between spin glass and spin liquid?

What is the difference between spin glass and spin liquid? Do they both originate from frustration?
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Intuition for when the replica trick should work and why it works

I am a graduate student in mathematics working in probability (without a very good background in physics honestly) and I've started to see arguments based on computations derived from the replica ...
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105 views

Does the spin glass corresponding to a restricted Boltzmann machine have a characteristic timescale?

From what I gather, a Boltzmann machine can be identified with a spin glass. Though I don't know the details yet (and would welcome any references within the last 5 years--not, e.g. MacKay, etc.), I ...