Related papers: Cluster derivation of Parisi's RSB solution for di…
We propose a simple scaling ansatz for the full replica symmetry breaking solution of the Sherrington-Kirkpatrick model in the low energy sector. This solution is shown to become exact in the limit x->0, x>>T of the Parisi replica symmetry…
In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap.…
Energy spectra of disordered systems share a common feature: if the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between…
Most natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics…
The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
Some recent results concerning the Sherrington-Kirkpatrick model are reported. For $T$ near the critical temperature $T_c$, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in…
We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscillate as the system size increases. While the extensive part…
The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz…
In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
The effects of quenched disorder on a single and many active run-and-tumble particles is studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
An outline of Morita's equilibrium ensemble approach to disordered systems is given, and hitherto unnoticed relations to other, more conventional approaches in the theory of disordered systems are pointed out. It is demonstrated to…
Extreme-value distributions are studied in the context of a broad range of problems, from the equilibrium properties of low-temperature disordered systems to the occurrence of natural disasters. Our focus here is on the ground-state energy…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
The coherent potential approximation, CPA, is a useful tool to treat systems with disorder. Cluster theories have been proposed to go beyond the translation invariant single-site CPA approximation and include some short range correlations.…
Disordered systems are an important class of models in statistical mechanics, having the defining characteristic that the energy landscape is a fixed realization of a random field. Examples include various models of glasses and polymers.…
We numerically simulate an oscillating Bose-Einstein condensate in a disordered trap [Phys. Rev. A 82, 033603 (2010)] and the results are in good agreement with the experiment. It allows us to verify that total energy and particle number…
In this Communication, we provide numerical evidence indicating that the standard single-reference coupled-cluster (CC) energies can be calculated alternatively to its copybook definition. We demonstrate that the CC energies can be…