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Universality in Polytope Phase Transitions and Message Passing Algorithms
Nonlinear mapping symmetric random matrix spin glass theory approximate messaging algorithm
2015/8/21
We consider a class of nonlinear mappings FA;N in RN indexed by symmetric random matrices A 2 RNN with independent entries. Within spin glass theory, special cases of these mappings correspond to ite...
Gibbs Measures and Phase Transitions on Sparse Random Graphs
Random graphs Ising model Gibbs measures Phase transitions Spin models Local weak convergence
2015/8/20
Many problems of interest in computer science and information theory can be phrased in terms of a probability distribution over discrete variables associated to the vertices of a large (but finite) sp...
Effective Action and Phase Transitions in Thermal Yang-Mills Theory on Spheres
Confinement Nonperturbative Effects QCD
2010/12/31
We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature
Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial cu...
A phase field model for liquid-vapour phase transitions
Liquid-Vapour Phase Transitions Critical point
2010/12/31
We propose a model describing the liquid-vapour phase transition according to a phase- eld approach. The model takes up the setting proposed in [1], where a phase eld ' is introduced whose equilibriu...
Striped periodic minimizers of a two-dimensional model for martensitic phase transitions
two-dimensional model martensitic phase transitions
2010/11/17
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by th...
On Quantum Markov Chains on Cayley tree II: Phase transitions for the associated chain with XY-model on the Cayley tree of order three
On Quantum Markov Chains Cayley tree II
2010/11/1
In the present paper we study forward Quantum Markov Chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By me...
On dynamical systems and phase transitions for $Q+1$-state $P$-adic Potts model on the Cayley tree
dynamical systems phase transitions
2010/11/1
In the present paper, we introduce a new kind of $p$-adic measures for $q+1$-state Potts model, called {\it $p$-adic quasi Gibbs measure}. For such a model, we derive a recursive relations with respe...
Fourier law, phase transitions and the stationary Stefan problem
Fourier law, phase transitions stationary Stefan problem
2010/9/1
We study the one-dimensional stationary solutions of an integro-differential equation derived by Giacomin and Lebowitz from Kawasaki dy-namics in Ising systems with Kac potentials, [5].
Oriented Site Percolation, Phase Transitions and Probability Bounds
Oriented site percolation Critical probability Phase transition Positive term power series
2008/6/27
We show that one half is a lower bound for the critical probability of an oriented site percolation process of Grimmett and Hiemer. This value improves the known lower bound of one third. We employ an...
Unified approach to evolution equations for non-isothermal phase transitions
Evolution equation Phase field Non-isothermal transitions
2007/12/31
The purpose of the paper is to set up a scheme which embodies and generalizes a wide class of phase-transition models and, moreover, provides a direct approach which avoids ad-hoc assumptions. The sta...
Stability and Existence of Multidimensional Subsonic Phase Transitions
multidimensional subsonic phase transitions
2007/12/10
The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to estab...