Related papers: Disordered Field Theory in $d=0$ and Distributiona…
In this note I revisit the calculation of partition function of simple one dimensional systems solvable by Bethe Ansatz. Particularly I show that by the precise definition and treatment of the partition function the nontrivial normalization…
Diffusive operations, which mix the populations of different elements of phase space, can irreversibly transform a given initial state into any of a spectrum of different states from which no further energy can be extracted through…
Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of…
Topological charge distributions in 2 dimensional CP^2 model with theta-term is calculated. In strong coupling regions, topological charge distribution is approximately given by Gaussian form as a function of topological charge and this…
A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a specific kind of quenched disorder is investigated, using the first principles nonperturbative quantum Monte Carlo calculations (QMC). The employed disorder…
We show how to define and calculate the ground state energy of a system of quantum particles with delta attractive interactions when the number of particles n$is non-integer. The question is relevant to obtain the probability distribution…
The crystalline ferromagnet with dipole-dipole interactions is studied within the framework of the three-dimensional random-field Ising model. The field distribution function and the analytic expression for temperature dependent free energy…
Massless quantum electrodynamics is studied at high temperature and zero chemical potential. We compute the Debye screening mass to order $e^{4}$ and the free energy to order $e^{5}$} by an effective field theory approach, recently…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
We define a "renormalized energy" as an explicit functional on arbitrary point configurations of constant average density in the plane and on the real line. The definition is inspired by ideas of [SS1,SS3]. Roughly speaking, it is obtained…
A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series…
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…
A polydisperse system contains particles with at least one attribute $\sigma$ (such as particle size in colloids or chain length in polymers) which takes values in a continuous range. It therefore has an infinite number of conserved…
The massive scalar field with $\lambda\varphi^4$ interaction placed in $(3+1)$ dimensional box is considered. The sizes of the box are $V\times \beta$ $(V=L^3$ is the volume, $T=1/\beta$ is the temperature). The free energy is evaluated up…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
We construct a dynamical field theory for noninteracting Brownian particles in the presence of a quenched Gaussian random potential. The main variable for the field theory is the density fluctuation which measures the difference between the…
We develop a classical density functional theory (DFT) for two site associating fluids in spatially uniform external fields which exhibit orientational inhomogeneities. The Helmholtz free energy functional is obtain using Wertheim's…
We compute the probability of positive large deviations of the free energy per spin in mean-field Spin-Glass models. The probability vanishes in the thermodynamic limit as $P(\Delta f) \propto \exp[-N^2 L_2(\Delta f)]$. For the…
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…