Related papers: Thermodynamic Limit for Mean-Field Spin Models
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
We study finite temperature properties of a generic spin-orbital model relevant to transition metal compounds, having coupled quantum Heisenberg-spin and Ising-orbital degrees of freedom. The model system undergoes a phase transition,…
By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend…
For general quantum systems the power expansion of the Gibbs potential and consequently the power expansion of the self energy is derived in terms of the interaction strength. Employing a generalization of the projector technique a compact…
Although the fully connected Ising model does not have a length scale, we show that its critical exponents can be found using finite size scaling with the scaling variable equal to N, the number of spins. We find that at the critical…
We discuss the dynamics and thermodynamics of the Brownian Mean Field (BMF) model which is a system of N Brownian particles moving on a circle and interacting via a cosine potential. It can be viewed as the canonical version of the…
The Hamiltonian Mean Field model describes a system of N fully-coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the…
In this paper we study a general class of hybrid mathematical models of collective motions of cells under the influence of chemical stimuli. The models are hybrid in the sense that cells are discrete entities given by ODE, while the…
We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is…
We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical…
We study mean-field classical $N$-vector models, for integers $N\ge 2$. We use the theory of large deviations and Stein's method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the…
We consider vector spin glasses whose energy function is a Gaussian random field with covariance given in terms of the matrix of scalar products. For essentially any model in this class, we give an upper bound for the limit free energy,…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
It is often incorrectly assumed that the number of microstates \Omega (E,V,N,...) available to an isolated system can have arbitrary dependence on the extensive variables E,V,N, .... However, this is not the case for natural systems which…
We consider the thermodynamical limit of a gl(N) spin chain with arbitrary representation at each site of the chain. We consider excitations (with holes and new strings) above the vacuum and compute their corrections in 1/L to the densities…
In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despite being arguably the simplest class of disordered quantum…
I show that spin-charge separation in 2-D t-J model leads to an increase of kinetic energy. Using a sum rule, I derive an exact expression for the lowest possible KE (E_{bound}) for any state without doubly occupied sites. KE of relevant…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
We consider a system of hierarchical interacting spins under dynamics of spin-flip type with a ferromagnetic mean field interaction, scaling with the hierarchical distance, coupled with a system of linearly interacting hierarchical…
We examine the stiffness of the Heisenberg spin-glass (SG) model at both zero temperature (T=0) and finite temperatures ($T \ne 0$) in three dimensions. We calculate the excess energies at T=0 which are gained by rotating and reversing all…