Phase transitions in three-dimensional systems

Giorgio Parisi A

Giorgio Parisi A

Kjetil Børkje, Steinar Kragset, Asle Sudbø

The existence of a discontinuity in the inverse dielectric constant of the two-dimensional (2D) Coulomb gas is demonstrated on purely numerical grounds. This is done by expanding the free energy in an applied twist and performing a finite-size scaling analysis of the coefficients of higher-order terms. The phase transition, driven by unbinding of dipoles, corresponds to the Kosterlitz-Thouless transition in the 2D $XY$ model. The method developed is also used for investigating the possibility of a Kosterlitz-Thouless phase transition in a three-dimensional system of point charges interacting with a logarithmic pair-potential, a system related to effective theories of low-dimensional strongly correlated systems. We also contrast the finite-size scaling of the fluctuations of the dipole moments of the two-dimensional Coulomb gas and the three-dimensional logarithmic system to those of the three-dimensional Coulomb gas.

William R. Schief

Michael N. Barber

Akai Kurbanovich Murtazaev, Albert Babaevich Babaev

On the basis of a histogram data analysis, phase transitions (PTs) in a three-dimensional diluted ferromagnetic 3- and 4-state Potts models are investigated. Systems with linear dimensions of L = 20–60 and spin concentrations of p = 1.00, 0.95, and 0.65 are studied. It is shown that the introduction of weak disorder ( p ∼ 0.95) into the system in the three-dimensional Potts model with q = 3 is sufficient to change a first-order phase transition to a second-order one, whereas, in the three-dimensional Potts model with q = 4, the change of a first-order phase transition to a second-order one occurs only in the presence of strong disorder ( p ∼ 0.65).