Related papers: Replica analysis of partition-function zeros in sp…
We study spin-glass systems characterized by continuous occurrence of singularities. The theory of Lee-Yang zeros is used to find the singularities. By using the replica method in mean-field systems, we show that two-dimensional…
The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
We investigate partition-function zeros of the many-body interacting spherical spin glass, the so-called $p$-spin spherical model, with respect to the complex temperature in the thermodynamic limit. We use the replica method and extend the…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
The Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems. An exact recurrence relation for the partition function is derived. It is shown that zeros of the partition…
We characterize the breaking of analyticity with respect to the replica number which occurs in random energy models via the complex zeros of the moment of the partition function. We perturbatively evaluate the zeros in the vicinity of the…
Zeros of the $n$th moment of the partition function $[Z^n]$ are investigated in a vanishing temperature limit $\beta \to \infty$, $n \to 0$ keeping $y=\beta n \sim O(1)$. In this limit, the moment parameterized by $y$ characterizes the…
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a…
We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer…
This contribution is devoted to cover some technical aspects related to the use of the recently proposed energy probability distribution zeros in the study of phase transitions. This method is based on the partial knowledge of the partition…
We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched…
We investigate the phase structure of the random-field Ising model with a bimodal random field distribution. Our aim is to test for the possibility of an equilibrium spin-glass phase, and for replica symmetry breaking (RSB) within such a…
We study the thermodynamic properties and the phase diagrams of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. It is a two-sublattice version of the ferromagnetic spherical p-spin glass model. We…
Binary mixtures of large and small particles with disparate size ratio exhibit a rich phenomenology at their glass transition points. In order to gain insights on such systems, we introduce and study a two-component version of the $p$-spin…
A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse…
The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an…
A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…