We derive the exact expression for the zero-field susceptibility of each spin of the Ising model on the scale-free (SF) network having the degree distribution P(k)∝k−γ with the Cayley tree-like structure. The system shows that: (i) the zero-field susceptibility of a spin in the interior...

The gauge theory of spin glasses and statistical–mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation functions and on the distribution functions of order...

Exact and/or rigorous results are reviewed for the Ising and XY/Villain spin glasses in finite dimensions, such as the exact energy, correlation identities and a functional relation between the distribution functions of ferromagnetic and spin glass order parameters. This last relation is useful...

After a brief introduction to information theory, we review the close relationship between the theory of spin glasses and information processing, error-correcting codes in particular. An interesting equivalence of the solvability condition of the spin glass problem and the optimal inference...

We calculate several correlation functions and distribution functions of dynamical variables for the gauge glass and the Villain model using the spin wave approximation and the gauge transformation. The results show that the spin wave approximation gives the exact solutions on the Nishimori line...

Quantum annealing is a novel method for combinatorial optimization problems. In this paper, we discuss the appropriate choice of quantum fluctuations in quantum annealing. The existence of room of choices of quantum fluctuations is an advantage of quantum annealing over simulated annealing. We...

We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the duality relation, the replica method, and the gauge...

The transition point of the five-state discrete vector model (planar Potts model) in two spatial dimensions is determined exactly by using a duality transformation. Also a comment is made on the justification of the uniqueness assumption of the transition point by the real space renormalization...

A variety of exact and rigorous results are derived for statistical-mechanical models of gauge glasses and their generalizations. In particular, I prove the absence of gauge glass ordering in two dimensions at finite temperatures. I also calculate the exact value of the internal energy in a...