Related papers: Equilibrium statistical mechanics of bipartite spi…
We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the…
Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants,…
We consider a bipartite mean-field model in which both the interaction constant and the external field take different values only depending on the groups particles belong to. We compute the exact value of the thermodynamic limit of the…
For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…
The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper,…
We combine theoretical and experimental efforts to propose a method for studying energy fluctuations, in particular, to obtain the related bi-stochastic matrix of transition probabilities by means of simple measurements at the end of a…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generality, we discuss the reduction of a Hamilton-Jacobi theory for…
In this work we give a proof of universality with respect to the choice of the statistical distribution of the quenched noise, for mean field bipartite spin glasses. We use mainly techniques of spin glasses theory, as Guerra's interpolation…
The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally…
The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…
At low temperatures the configurational phase space of a macroscopic complex system (e.g., a spin-glass) of $N\sim 10^{23}$ interacting particles may split into an exponential number $\Omega_s \sim \exp({\rm const} \times N)$ of ergodic…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
Out of thermal equilibrium, an environment imposes effective mechanical forces on microscopical nanofabricated devices, chemical or biological systems. Here we address the question of how to calculate these forces together with the response…
We study the low temperature dynamics of a two dimensional short-range spin system with uniform ferromagnetic interactions, which displays glassiness at low temperatures despite the absence of disorder or frustration. The model has a dual…
We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the…
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses. Our results characterize the maximum value attained by algorithms that are suitably Lipschitz with respect to the disorder through a variational…
This work proves an upper bound for the free energy of the Sherrington-Kirkpatrick model and its generalizations in terms of the Thouless-Anderson-Palmer (TAP) energy. The result applies to models with spherical or Ising spins and any mixed…
We study a variant of the Sherrington-Kirkpatrick (S-K) spin glass model with external field, where the random symmetric couplings matrix does not consist of i.i.d. entries but is instead orthogonally invariant in law. For sufficiently high…
In this paper, we study the Crisanti-Sommers variational problem, which is a variational formula for the free energy of spherical mixed $p$-spin glasses. We begin by computing the dual of this problem using a min-max argument. We find that…