Related papers: The Distributional Zeta-Function in Disordered Fie…
We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over…
We present a nonperturbative analysis of the weak- and strong-disorder regimes of the continuous random-field Ising model using the distributional zeta-function method. By performing the quenched-disorder average at the level of the…
The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…
The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to…
Dynamical mean field theory (DMFT) is a tool that allows to analyze the stochastic dynamics of $N$ interacting degrees of freedom in terms of a self-consistent $1$-body problem. In this work, focusing on models of ecosystems, we present the…
The partition function of the random energy model at inverse temperature $\beta$ is a sum of random exponentials $Z_N(\beta)=\sum_{k=1}^N \exp(\beta \sqrt{n} X_k)$, where $X_1,X_2,...$ are independent real standard normal random variables…
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method.…
The two dimensional $CP^1$ model with $\theta$ term is simulated. We compute the topological charge distribution $P(Q)$ by employing the ``set method" and ``trial function method", which are effective in the calculations for very wide range…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
We extract values for the free symmetry energy as a function of the fragment size (the proton number Z) from antisymmetrized molecular dynamics (AMD) calculations of calcium collisions. Simple statistical physics describe well the…
We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the n-th moment <Z^n> of the partition function is given by the ground state energy…
The recently introduced nested sampling algorithm allows the direct and efficient calculation of the partition function of atomistic systems. We demonstrate its applicability to condensed phase systems with periodic boundary conditions by…
We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters.…
The explicit expression for the two time free energy distribution function in one-dimensional random directed polymers is derived in terms of the Bethe ansatz replica technique. It is show that such type of the distribution function can be…
In the Sherrington-Kirkpatrick mean field model for spin glasses, we show that the quenched average of the free energy can be expressed through a couple of functional order parameters, in a form very similar to the one found in the frame of…
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…
The explicit expression for the two-time free energy distribution function in one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated problem to the…
In this paper, we consider an extended Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model, which is expressed as the summation of all Wilson loops on the graph, turns out to be represented by the…
We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from…