Related papers: Replica analysis of partition-function zeros in sp…
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of…
We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…
The distribution of the zeros of the partition function in the complex temperature plane (Fisher zeros) of the two-dimensional Q-state Potts model is studied for non-integer Q. On $L\times L$ self-dual lattices studied ($L\le8$), no Fisher…
The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…
We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…
The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two…
Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous…
We propose a method for calculating the Franz-Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the…
We suggest a new mean field method for studying the thermodynamic competition between magnetic and superconducting phases in a two-dimensional square lattice. A partition function is constructed by writing microscopic interactions that…
The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We study the random energy model with a hierarchical structure known as the generalized random energy model (GREM). In contrast to the original analysis by the microcanonical ensemble formalism, we investigate the GREM by the canonical…
Spin-glass theory is one of the leading paradigms of complex physics and describes condensed matter, neural networks and biological systems, ultracold atoms, random photonics, and many other research fields. According to this theory,…
Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution,…
A spin-1 model, appropriated to study the competition between bilinear (J_{ij}S_{i}S_{j}) and biquadratic (K_{ij}S_{i}^{2}S_{j}^{2}) random interactions, both of them with zero mean, is investigated. The interactions are infinite-ranged and…
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the…
The formalism of particle number on a spatial domain for mean field wave functions with pairing is revisited to account for the case where finite dimensional basis are used. The formulas differ from the ones previously used in the…
We derive the zero-temperature phase diagram of spin glass models with a generic fraction of ferromagnetic interactions on the Bethe lattice. We use the cavity method at the level of one-step replica symmetry breaking (1RSB) and we find…
Most of the analytical studies on spin glasses are performed by using mean-field theory and renormalization group analysis. Analytical studies on finite-dimensional spin glasses are very challenging. In this short note, a possible exten-…
Simulational studies of spin glasses in the last decade have focussed on the so-called replicon exponent $\alpha$ as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking…