Related papers: Solvable statistical models on a random lattice
Motivated by earlier numerical evidence for a percolation-like transition in space-time jamming, we present an analytic description of the transient dynamics of the deterministic traffic model elementary cellular automaton rule 184…
In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via}…
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 investigate a class of random graph ensembles based on the Feynman graphs of multidimensional integrals, representing statistical-mechanical partition functions. We show that the resulting ensembles of random graphs strongly resemble…
Details are presented of a recently announced exact solution of a model consisting of triangular trimers covering the triangular lattice. The solution involves a coordinate Bethe Ansatz with two kinds of particles. It is similar to that of…
A drift-kinetic model to describe the plasma dynamics in the scrape-off layer region of tokamak devices at arbitrary collisionality is derived. Our formulation is based on a gyroaveraged Lagrangian description of the charged particle…
We obtain a new solution of the star-triangle relation with positive Boltzmann weights which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines…
We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as…
We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the…
We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The…
We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with,…
We review models of random geometries based on the dynamical lattice approach. We discuss one dimensional model of simplicial complexes (branched polymers), two dimensional model of dynamical triangulations and four dimensional model of…
We introduce quantum dimer models on lattices made of corner-sharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimer-liquid phase with…
In this paper, we construct solvable ice models (six-vertex models) with stochastic weights and U-turn right boundary, which we term ``stochastic symplectic ice''. The models consist of alternating rows of two types of vertices. The…
The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…
Our work deals with symmetric rational functions and probabilistic models based on the fully inhomogeneous six vertex (ice type) model satisfying the free fermion condition. Two families of symmetric rational functions $F_\lambda,G_\lambda$…
Dyson has shown an equivalence between infinite-range Coulomb gas models and classical random matrix ensembles for the study of eigenvalue statistics. In this paper, we introduce finite-range Coulomb gas (FRCG) models as a generalization of…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the…
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important…