相关论文: Free energy of disordered urn models in the canoni…

We study the spin glass system consisting of a Random Energy Model coupled with a random magnetic field. This system was investigated by de Oliveira Filho, da Costa and Yokoi (Phys. Rev. E 74 [2006]) who computed the free energy. In this…

Using a formalism based on the spectral decomposition of the replicated transfer matrix for disordered Ising models, we obtain several results that apply both to isolated one-dimensional systems and to locally tree-like graph and factor…

Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian,…

We present a novel Path Integral Monte Carlo scheme to solve the Fr\"ohlich polaron model. At intermediate and strong electron-phonon coupling, the polaron self-trapping is properly taken into account at the level of an effective action…

Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of…

We discuss the use of the replica ansatz in computing free energies in random matrix theory, and confirm a conjectured condition on analytic continuation in the replica index at large-N.

A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a…

We investigate equilibrium statistical properties of urn models with disorder. Two urn models are proposed; one belongs to the Ehrenfest class, and the other corresponds to the Monkey class. These models are introduced from the view point…

We compute the quenched free energy in the Gaussian random matrix model by directly evaluating the matrix integral without using the replica trick. We find that the quenched free energy is a monotonic function of the temperature and the…

Taking advantage of the advances in generative deep learning, particularly normalizing flow, a framework, called Boltzmann Generator, has recently been proposed for the purpose of generating equilibrium atomic configurations from the…

One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…

For generalized 2D Ising model in an external magnetic field with the interaction of nearest neighbors, next nearest neighbors, all kinds of triple interactions and the quadruple interaction the formulas for finding free energy per lattice…

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.…

The generalized P\`olya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with diagonal replacement matrix, which arise in…

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in…

Inspired by the recent development on calculating the free energy change via a relaxation process [Nat. Phys. 14, 842 (2018)], we investigate the role of heat released in an irreversible relaxation following a large perturbation. Utilizing…

The excess free energy of a molecular cluster is a key quantity in models of the nucleation of droplets from a metastable vapour phase; it is often viewed as the free energy arising from the presence of an interface between the two phases.…

We consider a simple model to describe the widths of the mode locked intervals for the critical circle map. Using two different partitions of the rational numbers, based on Farey series and Farey tree levels respectively, we calculate the…

We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified…

In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to…