Related papers: Replica structure of one--dimensional Ising models
In this paper we discuss a disordered $d$-dimensional Euclidean $\lambda\varphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield…
We discuss an approach to compute the first and second moments of the number of eigenvalues $I_N$ that lie in an arbitrary interval of the real line for $N \times N$ Gaussian random matrices. The method combines the standard…
We study a family of Ising perceptron models with $\{0,1\}$-valued activation functions. This includes the classical half-space models, as well as some of the symmetric models considered in recent works. For each of these models we show…
We derive the analytical expression for the first finite size correction to the average free energy of disordered Ising models on random regular graphs. The formula can be physically interpreted as a weighted sum over all non…
We apply a generalized numerical transfer-matrix method to the 2-d Ising ferro- magnet in a nonzero field to obtain complex constrained free energies. Below $T_c$ certain eigenstates of the transfer matrix are identified as representing a…
Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica…
We consider the Ising model and the directed walk on two-dimensional layered lattices and show that the two problems are inherently related: The zero-field thermodynamical properties of the Ising model are contained in the spectrum of the…
We introduce a one dimensional disordered Ising model which at zero temperature is characterized by a non-trivial, non-self-averaging, overlap probability distribution when the impurity concentration vanishes in the thermodynamic limit. The…
The Ising spin - S model on recursive p - polygonal structures in the external magnetic field is considered and the general form of the free energy and magnetization for arbitrary spin is derived. The exact relation between the free…
In this article, we study an elastic manifold in quenched disorder in the limit of zero temperature. Naively it is equivalent to a free theory with elasticity in Fourier-space proportional to k^4 instead of k^2, i.e. a model without…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a…
Sigma models arise frequently in particle physics and condensed-matter physics as low-energy effective theories. In this paper I compute the exact free energy at any temperature in two hierarchies of integrable sigma models in two…
We solve the fermionic version of the Ising spin glass for arbitrary filling \mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from \mu to the anisotropy parameter D, we also obtain the…
Simple recursion relations for zero energy states of supersymmetric matrix models are derived by using an unconventional reducible representation for the fermionic degrees of freedom.
We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of…