Related papers: A curious relationship between Potts glass models
In these lectures I will review the approach to glasses based on the replica formalism. Many of the physical ideas are very similar to those of older approaches. The replica approach has the advantage of describing in an unified setting…
We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the…
We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random $p$-uniform hypergraphs with sparsity parameter $\alpha$. Our result shows that there exist two key regimes in which…
For the dynamical glassy transition in the $p$-spin mean field spin glass model a thermodynamic description is given. The often considered marginal states are not the relevant ones for this purpose. This leads to consider a cooling…
Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…
On approaching the dynamical transition temperature, supercooled liquids show heterogeneity over space and time. Static replica theory investigates the dynamical crossover in terms of the free energy landscape (FEL). Two kinds of static…
In this talk, after a short phenomenological introduction on glasses, I will describe some recent progresses that have been done in glasses using the replica method in the definition and in the evaluation of the configurational entropy (or…
We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass…
We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low…
We have considered the two-spin interaction spherical spin-glass model with asymmetric bonds (coupling constants). Besides the usual interactions between spins and bonds and between the spins and a thermostat with temperature $T_{\sigma}$…
Recently, Mori [Phys. Rev. E 84, 031128 (2011)] has conjectured that the free energy of Ising spin glass models with the Kac potential in the non-additive limit, such as the power-law potential in the non-additive regime, is exactly equal…
In certain mean field models for spin glasses there occurs a one step replica symmetry breaking pattern. As an example of general $1/N$-corrections in such systems, the fluctuations in the internal energy are calculated. For this specific…
We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle…
These lecture notes focus on the mean field theory of spin glasses, with particular emphasis on the presence of a very large number of metastable states in these systems. This phenomenon, and some of its physical consequences, will be…
We utilize the generalized entropy theory (GET) of glass formation to address one of the most singular and least understood properties of polymer glass-forming liquids in comparison to atomic and small molecule liquids -- the often…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…
Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature, the non-exponential…
We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a…
The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview…
The high temperature phase of the three dimensional random field Ising model is studied using replica symmetry breaking framework. It is found that, above the ferromagnetic transition temperature T_f, there appears a glassy phase at…