Related papers: Replica analysis of partition-function zeros in sp…
We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal across the entire High density phase and Low density phase. We…
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry…
We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is…
The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural…
We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the…
The site-random Ising spin glass model is investigated. We find a rigorous symmetry for the SG correlation and the free energy, which provides some restrictions in the phase diagram. Using the defect energies calculated by the numerical…
We define a replica field theory describing finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. A general analysis of this…
Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment…
We extend the circle theorem on the zeros of the partition function to a continuum system. We also calculate the exact zeros of the partition function for a finite system where the probability distribution for the order parameter is given…
Qualitative and quantitative information about critical phenomena is provided by the distribution of zeros of the partition function in the complex plane. We apply this idea to Ising models on non-periodic systems based on substitution. In…
Two, replica symmetry breaking specific, quantities of the Ising spin glass --- the breakpoint x1 of the order parameter function and the Almeida-Thouless line --- are calculated in six dimensions (the upper critical dimension of the…
Steady state distribution functions can be used to calculate stability conditions for modes, radiation energy losses, and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true…
In this paper we try to estimate the lower critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
We study numerically, the distribution of the zeros of the grand partition function of $k$-mers on a $k \times L$ strip in the complex activity (z) plane. Using transfer matrix methods, we find that our results match the analytical…
In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
An expression for the moment of partition function valid for any finite system size $N$ and complex power $n (\Re(n)>0)$ is obtained for a simple spin glass model termed the {\em discrete random energy model} (DREM). We investigate the…
The nature of polyamorphism and amorphous-to-amorphous transition is investigated by means of an exactly solvable model with quenched disorder, the spherical s+p multi-spin interaction model. The analysis is carried out in the framework of…
We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase…