Related papers: A solvable problem in statistical mechanics: the d…
We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
Aim of this paper is to give an extensive treatment of bipartite mean field spin systems, ordered and disordered: at first, bipartite ferromagnets are investigated, achieving an explicit expression for the free energy trough a new minimax…
A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the mean-field phi^4-model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase…
The ground state energy and entropy of the dilute mean field Ising model is computed exactly by a single order parameter. An analogous exact solution is obtained in presence of a magnetic field with random locations. Results allow for a…
In this article, using a known method, a computation is performed of the derivatives of the microcanonical entropy, with respect to the energy up to the 4-th order, using a Laplace transform technique, and adapted it to the case where the…
Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices…
We study canonical-equilibrium properties of Random Field $O(n)$ Models involving classical continuous vector spins of $n$ components with mean-field interactions and subject to disordered fields acting on individual spins. To this end, we…
We propose a formally exact statistical field theory for describing classical fluids with ingredients similar to those introduced in quantum field theory. We consider the following essential and related problems : i) how to find the correct…
Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the…
We consider the mean field analog of the p-star model for homogeneous random networks, and compare its behaviour with that of the p-star model and its classical mean field approximation in the thermodynamic regime. We show that the…
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…
It has been proved for a class of mean-field and long-range systems that the concavity of the thermodynamic entropy determines whether the microcanonical and canonical ensembles are equivalent at the level of their equilibrium states, i.e.,…
We study the capacity of entanglement in the microcanonical ensemble for an effectively additive bipartite system. Using typicality and the block structure of the microcanonical reduced state, we show that in the thermodynamic regime the…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann-Planck's principle,…
Aggregation transitions in disordered mesoscopic systems play an important role in several areas of knowledge, from materials science to biology. The lack of a thermodynamic limit in systems that are intrinsically finite makes the…
We use the mean-field approximation to simplify the master equation for sympathetic cooling of Bosons. For the mean single-particle occupation numbers, this approach yields the same equations as the factorization assumption introduced in an…
We study the statistical physics of the classical Ising model in the so-called $\alpha$-R\'enyi ensemble, a finite-temperature thermal state approximation that minimizes a modified free energy based on the $\alpha$-R\'enyi entropy. We begin…
We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical…
An exact analytical solution of generalized three-state double-chain Potts model with multi-spin interactions which are invariant under cyclic shift of all spin values is obtained. The partition function in a finite cyclically closed strip…