Search results for "Potts model"
showing 4 items of 34 documents
Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions
2000
The clustering of companies within a specific stock market index is studied by means of super-paramagnetic transitions of an appropriate q-state Potts model where the spins correspond to companies and the interactions are functions of the correlation coefficients determined from the time dependence of the companies' individual stock prices. The method is a generalization of the clustering algorithm by Domany et. al. to the case of anti-ferromagnetic interactions corresponding to anti-correlations. For the Dow Jones Industrial Average where no anti-correlations were observed in the investigated time period, the previous results obtained by different tools were well reproduced. For the Standa…
Ordering and demixing transitions in multicomponent Widom-Rowlinson models.
1995
We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not …
Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations
2012
The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed, and as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL square lattices (40<=L<=100) are presented. It is shown that the microcanonical ensemble is well-suited both to find the precise location of the first order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heatbath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature vers…
From orientational glasses to structural glasses: What computer simulations have contributed to understand experiments
2002
Abstract Orientational glasses, produced by random dilution of molecular crystals, exhibit a freezing transition of the quadrupole moments. Monte Carlo simulations of lattice models (generalization of the Edwards–Anderson spin glass model) have been used to elucidate this behavior. While short range models exhibit a static glass transition at zero temperature only, the infinite range Potts glass exhibits a transition where a glass order parameter appears discontinuously. At higher temperature, a dynamical transition occurs, described by mode-coupling theory (MCT). MCT has also been tested by Monte Carlo and molecular dynamics simulations of coarse-grained models of glass-forming polymers. W…