Related papers: The Hopfield Model with Superlinearly Many Pattern…
Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2-…
We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of $\beta t$, $w=\exp{(-\beta U)}$ and ${1\over \beta U}$ for arbitrary filling. The expansions are done in the grand canonical ensemble and are…
In this short note, we prove a central limit theorem for the free energy in the Ghatak- Sherrington model at high enough temperatures, based on a generalization of the stochastic calculus method for the SK model derived in [CN95, Tin05].
In this note, we consider the multi-species Sherrington-Kirkpatrick spin glass model at its conjectured critical temperature, and we show that, when the variance profile matrix $\Delta^2$ is positive semi-definite, the variance of the free…
The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this…
In this paper we study the large-Z behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy sqrt(p^2c^2+m^2c^4)-mc^2. We prove that to leading order in Z the energy is the same as in the…
We study the Cauchy directed polymer model on $\mathbb{Z}^{1+1}$, where the underlying random walk is in the domain of attraction to the $1$-stable law. We show that, if the random walk satisfies certain regularity assumptions and its…
We present an extensive numerical study of the Sherrington-Kirkpatrick model in transverse field. Recent numerical studies of quantum spin-glasses have focused on exact diagonalization of the full Hamiltonian for small systems ($\approx$ 20…
We analyze the thermodynamics and the critical behavior of the supersymmetric su($m$) $t$-$J$ model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for…
We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the…
We study the three-band Hubbard model for the copper oxide plane of the high-temperature superconducting cuprates using determinant quantum Monte Carlo and the dynamical cluster approximation (DCA) and provide a comprehensive view of the…
We investigate the grand potential of the one-dimensional Hubbard model in the high temperature limit, calculating the coefficients of the high temperature expansion ($\beta$-expansion) of this function up to order $\beta^4$ by an…
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric…
We consider an arbitrary translationally invariant chain model with nearest neighbors interaction and satisfying periodic boundary condition. The approach developed here allows a thermodynamic description of the chain model directly in…
Magnetic phenomena of the superantiferromagnetic Ising model in both uniform longitudinal ($H$) and transverse ($\Omega $) magnetic fields are studied by employing a mean-field variational approach based on Peierls-Bogoliubov inequality for…
The spherical Sherrington-Kirkpatrick (SSK) model and its bipartite analog both exhibit the phenomenon that their free energy fluctuations are asymptotically Gaussian at high temperature but asymptotically Tracy-Widom at low temperature.…
In this paper, we study the high temperature or low connectivity phase of the Viana-Bray model. This is a diluted version of the well known Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric region, we obtain a…
We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising…
If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$ \omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2}) $$ for every decomposition $N_1+N_2=N$, then its free energy density…
We introduce and analyze free energy landscapes defined by associating to any point inside the sphere a free energy calculated on a thin spherical band around it, using many orthogonal replicas. This allows us to reinterpret, rigorously…