Related papers: On the TAP free energy in the mixed $p$-spin model…
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
We suggest a possible approach to proving the M\'ezard-Parisi formula for the free energy in the diluted spin glass models, such as diluted K-spin or random K-sat model at any positive temperature. In the main contribution of the paper, we…
In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
We use real replicas to investigate stability of thermodynamic homogeneity of the free energy of the Sherrington-Kirkpatrick (SK) model of spin glasses. Within the replica trick with the replica symmetric ansatz we show that the averaged…
We explore the energy content of superpositions of current states. Specifically, we focus on the maximum energy that can be extracted from them through local unitary transformations. The figure of merit we employ is the local ergotropy. We…
Magnetic effects on free electron systems have been studied extensively in the context of spin-to-orbital angular momentum conversion. Starting from the Dirac equation, we derive a fully relativistic expression for the energy of free…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
Magnetic properties of the 1D mixed spin-1/2 and spin-S (S >1/2) transverse Ising model in the presence of an external longitudinal magnetic field are calculated exactly by the use of the generalised decoration-iteration mapping…
By using the BRST supersymmetry we compute the quenched complexity of the TAP states in the SK model. We prove that the BRST complexity is equal to the Legendre transform of the static free energy with respect to the largest replica…
An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral…
In this paper we study two non-mean-field spin models built on a hierarchical lattice: The hierarchical Edward-Anderson model (HEA) of a spin glass, and Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the existence…
We derive a free energy for weakly anisotropic ferromagnets which is valid in the whole temperature range and interpolates between the micromagnetic energy at zero temperature and the Landau free energy near the Curie point T_c. This free…
This paper is devoted to a detailed study of a p-spins interaction model with external field, including some sharp bounds on the speed of self averaging of the overlap as well as a central limit theorem for its fluctuations, the…
We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, $\langle\cdot\rangle_N$, into a…
We establish relations between different characterizations of order in spin glass models. We first prove that the broadening of the replica overlap distribution indicated by a nonzero standard deviation of the replica overlap $R^{1,2}$…
We study mean-field spin glass models with general vector spins and convex covariance function. For those models, it is known that the limit of the free energy can be written as the supremum of a functional, this is the celebrated Parisi…
We consider ground state energies (GSE) of multipartite $p$-spin models. Relying on partially lifted random duality theory (pl RDT) concepts we introduce an analytical mechanism that produces easy to compute lower and upper GSE bounds for…
This is the first of a series of three papers about the Elastic Manifold model. This classical model proposes a rich picture due to the competition between the inherent disorder and the smoothing effect of elasticity. In this paper, we…
We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…