Application of p-adic analysis to models of spontaneous breaking of the replica symmetry

Abstract

Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) investigated using p-adic analysis.

Latex, 8 pages

Cited by in corpus (46)

• p-Adic Mathematical Physics
• p-Adic Models of Ultrametric Diffusion Constrained by Hierarchical Energy Landscapes
• p-Adic description of characteristic relaxation in complex systems
• $p$-Adic Mathematical Physics: The First 30 Years
• A p-Adic Model of DNA Sequence and Genetic Code
• p-Adic pseudodifferential operators and p-adic wavelets
• Genetic code on the dyadic plane
• On $p$-adic Gibbs measures of countable state Potts model on the Cayley tree
• Replica symmetry breaking related to a general ultrametric space III: the case of general measure
• First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
• Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
• Phase transitions for $P$-adic Potts model on the Cayley tree of order three
• Parabolic Type Equations and Markov Stochastic Processes on Adeles
• TASI lectures on complex structures
• $p$-adic discrete dynamical systems and their applications in physics and cognitive sciences
• Non-Degenerate Ultrametric Diffusion
• On $p$-adic Gibbs Measures for Hard Core Model on a Cayley Tree
• Renormalization method in $p$-adic $\lambda$-model on the Cayley tree
• The Arrhenius formula in kinetic theory and Witten's spectral asymptotics
• Fractal globule as an artificial molecular machine
• On scale-free and poly-scale behaviors of random hierarchical network
• Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes
• On metric structure of ultrametric spaces
• Non-Archimedean Replicator Dynamics and Eigen's Paradox
• Ultrametric theory of conformational dynamics of protein molecules in a functional state and the description of experiments on the kinetics of CO binding to myoglobin
• $p$-Adic Brownian Motion is a Scaling Limit
• Replica Symmetry Breaking without Replicas
• Spectral problem of block-rectangular hierarchical matrices
• On Infinitesimal Generators and Feynman-Kac Integrals of Adelic Diffusion
• On the motifs distribution in random hierarchical networks
• How the Quasispecies Evolution Depends on the Topology of the Genome Space
• Quantum-like formalism for cognitive measurements
• Random walk on p-$adics in glassy systems
• p-Adic numbers in bioinformatics: from genetic code to PAM-matrix
• p-Adic representation of the Cuntz algebra and the free coherent states
• Time-Varying Energy Landscapes and Temperature paths: Dynamic Transition Rates in locally Ultrametric Complex Systems
• Existence of $P$-adic quasi Gibbs measure for countable state Potts model on the Cayley tree
• Continuous-time quantum walks on ultrametric spaces
• Probabilistic pathway representation of cognitive information
• On phase transition for one dimensional countable state $P$-adic Potts model
• Hausdorff dimension and hierarchical system dynamics
• Landscape dynamics, interbasin kinetics and ultrametric diffusion
• Non-Archimedean Reaction-Ultradiffusion Equations and Complex Hierarchic Systems
• Coleman-Weinberg potential in $p$-adic field theory
• Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift
• $p$-adic boundary laws and Markov chains on trees