0
votes
0answers
25 views

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 ...
6
votes
2answers
163 views

Subtleties in the exact solution to the 1D quantum XY model, in particular the Bogoliubov transformation

I am writing programs to construct the spectra of models with known exact solutions, and soon noticed some subtleties that are not often mentioned in most references. These subtleties are not ...
0
votes
0answers
16 views

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 ...
2
votes
1answer
81 views

What happens to the free energy of the two-dimensional ising model with vortices?

The classical 2d Ising model has a Hamiltonian of the form: \begin{equation} H = -\sum_{m,n = 0}^{M,N} J_1 x_{m,n}x_{m+1,n} + J_2 x_{m,n}x_{m,n+1} \end{equation} The partition function for the model ...
5
votes
1answer
245 views

Interpretation of the 1D transverve field Ising model vacuum state in a spin-language

The 1D transverse field Ising model, \begin{equation} H=-J\sum_{i}\sigma_i^z\sigma_{i+1}^z-h\sum_{i}\sigma^x_i, \end{equation} can be solved via the Jordan-Wigner (JW) transformation (for further ...
0
votes
0answers
50 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?
4
votes
2answers
202 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
2
votes
1answer
187 views

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 ...
2
votes
1answer
43 views

Does an Ising lattice that returns to equilibrium create a current by induction?

Consider you have an Ising lattice with a dominant up component out of thermal equilibrium, that's your initial state. The down spins want to flip up and align with the ups, and they'll do so until a ...
5
votes
2answers
208 views

Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
2
votes
2answers
308 views

Identifying a critical phenomena?

I have a system with a number of measurables (in time). Some measurables are discrete some are continuous (within the measurement accuracy). How can I determine whether my system experiences ...