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arXiv:0812.1287 · Physical Review B

Spin glass phase in the four-state three-dimensional Potts model

Andrés De la Cruz, L. A. Fernández, A. Gordillo-Guerrero, Marco Guidetti, A. Maiorano, Filippo Mantovani, Enzo Marinari, Víctor Martín-Mayor, A. Muñoz Sudupe, Denis Navarro, Giorgio Parisi A, Sergio Perez-Gaviro, Juan Jesus Ruiz-Lorenzo, Sebastiano Fabio Schifano, Daniele Sciretti, Alfonso Tarancón, R. Tripiccione, José Luis Velasco, David Yllanes, A. P. Young

Published May 7, 2009• 16 citations

Abstract

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the ``random permutation'' Potts glass.

DOI: 10.1103/physrevb.79.184408

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We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the ``random permutation'' Potts glass.

We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulations and a finite-size scaling analysis. By using a field programmable gate array, we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in

d=4

and to study the critical properties of the transition. In

d=3

, our results are consistent with the presence of a Kosterlitz-Thouless transition, but also with different scenarios: transient effects due to a value of the lower critical dimension slightly below 3 could be very important.

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice

(L=20)

has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the \ensuremath{\nu} and \ensuremath{\eta} critical exponents are also presented.

We study the critical behavior of the short-range

p

-state Potts spin glass in three and four dimensions using Monte Carlo simulations. In three dimensions, for

p=3

, a finite-size scaling analysis of the correlation length shows clear evidence of a transition to a spin-glass phase at ${T}_{\mathrm{c}}\ensuremath{\simeq}0.273$ for a Gaussian distribution of interactions and ${T}_{\mathrm{c}}\ensuremath{\simeq}0.377$ for a $\ifmmode\pm\else\textpm\fi{}J$ (bimodal) distribution. These results indicate that the lower critical dimension of the three-state Potts glass is below 3. By contrast, the correlation length of the ten-state

(p=10)

Potts glass in three dimensions remains small even at very low temperatures and thus shows no sign of a transition. In four dimensions we find that the

p=3

Potts glass with Gaussian interactions has a spin-glass transition at ${T}_{\mathrm{c}}\ensuremath{\simeq}0.536$.