1,721,004 research outputs found
A Note on the Stability of Phase Diagrams in Lattice Systems
No full textWe construct a class of non-symmetry breaking pair interactions, which change the phase diagram of the n.n. Ising and classical XY model. Furthermore we improve earlier obtained constraints on the decrease of interactions, necessary to get analyticity properties of the pressure in manifolds of non-symmetry breaking interactions.
The Order Parameter in a Spin Glass
No full textVarious possible precise definitions of an Edwards-Anderson type of order parameter for an Ising model spin glass are considered, using boundary conditions for a finite system, states of an infinite system, and a duplicate-system approach. Several of these definitions are shown to yield identical results.
Chopper model of pattern recognition
Get PDFA simple model is proposed that allows an efficient storage and retrieval of random patterns. Also correlated patterns can be handled. The data are stored in an Ising-spin system with ferromagnetic interactions between all the spins and the main idea is to "chop" the system along the boundaries where the patterns differ.
Differentiability Properties of the Pressure in Lattice Systems
No full textIn two recent papers Ruelle gave a heuristic theory of phase transitions, using some techniques introduced by Israel. He proves a version of the Gibbs phase rule, assuming a differentiability condition for the pressure. Ruelle already pointed out that his condition cannot always hold. In this paper we prove that the interaction spaces which he considers are in general too large for his condition to hold. We also show that the version of the Gibbs phase rule which is a consequence of this condition does not hold in general. Moreover we give some constraints on the analyticity properties of the pressure.
A Note on the Stability of Phase Diagrams in Lattice Systems
No full textWe construct a class of non-symmetry breaking pair interactions, which change the phase diagram of the n.n. Ising and classical XY model. Furthermore we improve earlier obtained constraints on the decrease of interactions, necessary to get analyticity properties of the pressure in manifolds of non-symmetry breaking interactions
Chaotic Size Dependence in the Ising Model with Random Boundary Conditions
Get PDFWe study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.
On a Classical Spin Glass Model
No full textA simple, exactly soluble, model of a spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, but its solution can be obtained without replicas. As the temperature T is lowered, the spin-glass phase is reached via an equilibrium phase transition at T=Tf. The spin-glass magnetization exhibits a distinct S-shape character, which is indicative of a field-induced transition to a state of higher magnetization above a certain threshold field.
For suitable probability distributions of the exchange interactions.
(a) A mixed phase is found where spin-glass and ferromagnetism coexist.
(b) The zero-field susceptibility has a flat plateau for 0≤T≤Tf and a Curie-Weiss behaviour for T>Tf.
(c) At low temperatures the magnetic specific heat is linearly dependent on the temperature.
The physical origin of the dependence upon the probability distributions is explained, and a careful analysis of the ground state structure is given.
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