相关论文: Free energy of bipartite spherical Sherrington--Ki…
We discuss fluctuations near the second order phase transition where the free energy has an additional non-Hermitian term. The spectrum of the fluctuations changes when the odd-parity potential amplitude exceeds the critical value…
We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann.~Probab.~43~(2015), no.~6, 3494--3513, where the author proved the Parisi formula under…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
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…
When an isolated system is brought in contact with a heat bath its final energy is random and follows the Gibbs distribution -- a cornerstone of statistical physics. The system's energy can also be changed by performing non-adiabatic work…
We consider the $XYZ$ chain model of arbitrary spin $S$ in the high temperature region, with external magnetic field and single-ion anisotropy term. Our high-temperature expansion of the Helmholtz free energy is analytic in the parameters…
We give examples of modeling the string free energy whose behavior mimics that of QCD: a power-law at high temperature and an exponential decrease at low temperature. Although the effective description is in terms of strings, no limiting…
We study the L\'evy spin glass model, a fully connected model on $N$ vertices with heavy-tailed interactions governed by a power law distribution of order $0<\alpha<2.$ Our investigation is divided into three cases $0<\alpha<1$, $\alpha=1$,…
The Landau Free Energy determines the landscape of order parameter fluctuations that occur in a physical system at thermal equilibrium and, in particular, characterizes the critical phenomena. We propose a semi-analytical approach based on…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the…
The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme…
We compute higher order contributions to the free energy of noncommutative quantum electrodynamics at a nonzero temperature $T$. Our calculation includes up to three-loop contributions (fourth order in the coupling constant $e$). In the…
We calculate the real-time-correlation function of the Sherrington-Kirkpatrick spin-glass model in a transverse field. Using a careful analysis of the perturbative expansion of the functional-integral representation, we derive the…
We present a detailed analysis for the Langevin dynamics of a spherical spin-glass model (the spherical Sherrington-Kirkpatrick model). All the spins in the system are coupled by pairs via a random interaction matrix taken from the Gaussian…
We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy.…
The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states…
In the seminal work by G. Eilenberger [Z. Phys. 214, 195 (1968)], the quasiclassical expression for the free energy of spin-singlet superconductor has been suggested. Starting from the Luttinger-Ward formulation we derive the Eilenberger…
A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~…
In solving the problem of finding a temperature distribution which, at zero temperature, corresponds to superfluidity, i.e., to nonzero energy, the author tried to quantize free energy. This was done on the basis of supersecondary…