CMST 25(1) 31–39 (2019) DOI:10.12921/cmst.2018.0000053 Computation of latent heat in the system of multi-component order parameter: 3D Ashkin-Teller model D. Jeziorek-Kniola, Z. Wojtkowiak, G. Musial * Adam Mickiewicz University Faculty of Physics ul. Umultowska 85 61-614 Pozna´ n, Poland *E-mail: gmusial@amu.edu.pl Received: 13 November 2018; revised: 29 March 2019; accepted: 29 March 2019; published online: 31 March 2019 Abstract: The method for computing the latent heat in a system with many independently behaving components of the or- der parameter proposed previously is presented for a chosen point of the phase diagram of the 3D Ashkin-Teller (AH) model. Binder, Challa, and Lee-Kosterlitz cumulants are exploited and supplemented by the use of the energy distribution histogram. The proposed computer experiments using the Metropolis algorithm calculate the cumulants in question, the in- ternal energy and its partial contributions as well as the energy distribution for the model Hamiltonian and its components. The important part of our paper is an attempt to validate the results obtained by several independent methods. Key words: the standard 3D Ashkin-Teller model, temperature driven phase transitions, latent heat, high performance computing I. INTRODUCTION One of the basic thermodynamic quantities which en- ables examination of the character of a phase transition is la- tent heat. In this paper, we propose precise determination of the value of latent heat in the computer experiment based on various cumulants and a histogram of energy distribution. We exploit Binder [1], Challa [2] and Lee-Kosterlitz [3] cu- mulants as well as the internal energy distribution histogram method [3, 4] which were introduced for systems with one independent order parameter, such as the Ising like mod- els. The non-trivial generalization of the widely exploited Ising model of current interest is the Ashkin-Teller (AT) model [5] which is one of the most important models in sta- tistical physics and every year a dozen works are devoted to it (see e.g. [6–8] and the papers cited therein). More- over, the AT model shows the complex phase diagram and the Monte Carlo (MC) simulation results published so far suggest the possibility of the occurrence of the non-universal behavior also in the 3D AT model [9–12] which has been ob- served in the 2D one [13–16]. The AT lattice model has been proposed for four compo- nent mixtures [5], but the interest in it significantly increased after Fan’s work [17] who expressed it in terms of two Ising models put on the same lattice with spins s i and σ i at each lattice site i. As in the original Ising model, we take into ac- count only two-spin interactions of a constant magnitude J 2 between the nearest neighbors. These two independent Ising models are coupled by the four-spin interaction of a con- stant magnitude J 4 , also only between couples of nearest- neighboring spins, leading to the effective Hamiltonian H - H k B T = X [i,j] {K 2 (s i s j + σ i σ j )+ K 4 s i σ i s j σ j }. (1) In Eq. (1) K n = -J n /k B T , with n = 2 or 4, [i, j ] denotes summation over nearest-neighboring lattice sites, k B is the Boltzmann constant, and T is the temperature