Related papers: A general method to determine replica symmetry bre…
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…
It is shown that continuously changing the effective number of interacting particles in p-spin-glass-like model allows to describe the transition from the full replica symmetry breaking glass solution to stable first replica symmetry…
In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a…
In a recent letter Marinari et al [Phys. Rev. Lett. 81, 1698 (1998)] introduced a new method to study spin glass transitions and argued that by probing replica symmetry (RS) as opposed to time reversal symmetry (TRS), their method…
The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in \cite{RS} which show that two of these parameters, $G$ and $G_c$, take universal values in the $\lim_{T\to 0}$. In this…
Physical quantities in the mixed $p$-spin glasses are evaluated with Nishimori's gauge theory and several variance inequalities. The $\mathbb Z_2$-symmetry breaking and the replica-symmetry breaking are studied in finite and infinite…
The analysis of the solution with full replica symmetry breaking in the vicinity of $T_c$ of a general spin glass model with reflection symmetry is performed. The leading term in the order parameter function expansion is obtained. Parisi…
Within the Bethe- Peierls method the for short- ranged Ising spin glass, recently formulated by Serva and Paladin, the equation for the spin glass parameter function near the transition to the paramagnetic phase has been carried out. The…
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…
Finite-size effects in the mean-field Ising spin glass and the mean-field three-state Potts glass are investigated by Monte Carlo simulations. In the thermodynamic limit, each model is known to exhibit a continuous phase transition into the…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
The thermodynamics of the infinite-range Ising spin glass with p-spin interactions in the presence of an external magnetic field h is investigated analytically using the replica method. We give emphasis to the analysis of the transition…
The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica…
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
The full replica symmetry breaking free energy of the Ising spin glass on random regular graphs is given by the solutions of two auxiliary variational problems inside a global (physical) variational problem on the order parameter. In this…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…
We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the…
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a…
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an…