[figure: 9.7 cm]

MONTE CARLO SIMULATIONS OF THE 3D ASHKIN-TELLER

MODEL: CONTINUOUS PHASE TRANSITION LINES

G. Musiał, L. Dȩbski, G. Kamieniarz

Institute of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań,

                    Poland, e-mail: gulf@spin.amu.edu.pl

The Hamiltonian of the Ashkin-Teller model is −βH = H = ∑_{[i,j]}{K_{2}(s_{i}s_{j} + σ_{i}σ_{j}) + K_{4}s_{i}σ_{i}s_{j}σ_{j}}, where β = (k_{B}T)^{−1}, k_{B} is the Boltzmann’s constant, T the temperature, [i, j] denotes summation over nearest neighboring lattice sites and K_{i} are the couplings, with i = 2 or 4. In this paper we report the simulations of Monte Carlo type based on the invariance of the Binder cumulant Q, which is the ratio of the square of the second moment of the order parameter to its fourth moment, in the critical point [1]. The phase transition points T_{c} were determined from the analysis of the cumulant Q_{L} of cubic samples of the linear size L ≤ 30. Gibbs distribution was sampled using the Metropolis algorithm. Each point on the phase diagram was calculated using 10^{7} to 10^{8} MCS. We have applied the accurate estimates of the critical exponents of the 3D Ising model [1] in the finite-size-scaling analysis to calculate the locations of continuous phase transitions points on the (K_{4}, K_{2}) phase diagram of the 3D AT model. Owing to the application of finite-size-scaling analysis we not only allocated points on the phase diagram with a precision of at least 4 decimal digits, but also we confirmed the continuous Ising-like character of phase transitions.

[1] H.W.J. Blöte, E. Luijten, J.R. Heringa, J. Phys. A28 (1995) 6289

[figure: 13.4 cm]

Subject category :

5. Phase Transitions and Critical Phenomena

Presentation mode : oral

Corresponding author : Lech Dȩbski

Address for correspondence : Institute of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland, tel. (+48-61)8273030

Email address : gulf@spin.amu.edu.pl