0000000000372664

AUTHOR

Pierre Emmanuel Berche

showing 3 related works from this author

The McCoy-Wu model in the mean-field approximation

1998

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $\beta \approx 3.6$ and $\beta_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^{\omega}$ and we show that the difference between the values of the critical…

PhysicsStatistical Mechanics (cond-mat.stat-mech)FOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsDisordered Systems and Neural Networks (cond-mat.dis-nn)Condensed Matter - Disordered Systems and Neural NetworksPower lawOmegaSingularityMean field theoryCritical point (thermodynamics)ExponentSpontaneous magnetizationCritical exponentCondensed Matter - Statistical MechanicsMathematical PhysicsMathematical physicsJournal of Physics A: Mathematical and General
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Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models

1999

We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the nei…

PhysicsPhase transitionStatistical Mechanics (cond-mat.stat-mech)Monte Carlo methodDuality (optimization)FOS: Physical sciencesDisordered Systems and Neural Networks (cond-mat.dis-nn)Condensed Matter - Disordered Systems and Neural NetworksFixed pointCondensed Matter PhysicsCoupling (probability)Electronic Optical and Magnetic MaterialsTransition pointAperiodic graphStatistical physicsCondensed Matter - Statistical MechanicsPotts model
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Influence of deterministic fluctuations on the 8-state Potts model

1999

We study a layered 8-state Potts model with an aperiodic modulation of the exchange couplings. Depending on its geometric properties, the aperiodic sequence may induce a 2nd order phase transition.

SequencePhase transitionHardware and ArchitectureAperiodic graphModulation (music)General Physics and AstronomyState (functional analysis)Statistical physicsMathematicsPotts modelDeterministic system
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