Search for the Heisenberg spin glass on rewired square lattices with antiferromagnetic interaction

AIP Conference Proceedings

Komura

Okabe

2014

Phase transitions are ubiquitous phenomena, exemplified by the melting of ice and spontaneous magnetization of magnetic material. In general, a phase transition is associated with a symmetry breaking of a system; occurs due to the competition between coupling interaction and external fields such as thermal energy. If the phase transition occurs with no latent heat, the system experiences continuous transition, also known as second order phase transition. The ferromagnetic q-state Potts model with r extra invisible states, introduced by Tamura, Tanaka, and Kawashima [Prog. Theor. Phys. 124, 381 (2010)], is studied by using the Wang-Landau method. The density of states difference (DOSD), ln g(E + ∆E) − ln g(E), is used to investigate the order of the phase transition and examine the critical value of r changing the second to the first order transition.

Section: Resultsmentioning

confidence: 68%

Probing phase transition order of q-state Potts models using Wang-Landau algorithm

AIP Conference Proceedings

Komura

Okabe

2014

Critical properties of the antiferromagnetic Ising model on rewired square lattices

Yusuf

2018

J. Phys.: Conf. Ser.

Self Cite

Abstract. The effect of randomness on critical behavior is a crucial subject in condensed matter physics due to the the presence of impurity in any real material. We presently probe the critical behaviour of the antiferromagnetic (AF) Ising model on rewired square lattices with random connectivity. An extra link is randomly added to each site of the square lattice to connect the site to one of its next-nearest neighbours, thus having different number of connections (links). Average number of links (ANOL) κ is fractional, varied from 2 to 3, where κ = 2 associated with the native square lattice. The rewired lattices possess abundance of triangular units in which spins are frustrated due to AF interaction. The system is studied by using Monte Carlo method with Replica Exchange algorithm. Some physical quantities of interests were calculated, such as the specific heat, the staggered magnetization and the spin glass order parameter (Edward-Anderson parameter). We investigate the role played by the randomness in affecting the exisiting phase transition and its interplay with frustration to possibly bring any spin glass (SG) properties. We observed the low temperature magnetic ordered phase (Néel phase) preserved up to certain value of κ and no indication of SG phase for any value of κ. IntroductionThe cooperative phenomena are ubiquitous in nature, driven by the presence of coupling interaction between each individual constituent of materials [1,2]. This is exemplified by the spontaneous magnetization by which certain magnetic material is entering a ferromagnetic phase below its transition temperature T c (Curie temperature) and able to attract the nearby metals surrounding it. The high temperature disorded phase and the cooperative ordered phase at low temperature are separated by T c . A phase transition is essentially rendered by the competition between the external fields, such as temperature, which tend to destroy the order and the coupling interaction which tends to create order.Based on the nature of free energy function, a phase transition is grouped into the first and the second order phase transition [3]. The transition is called as first order if the first order derivative of the free energy of the system is discontinuous. If the derivative is continuous, the transition is second order, also called continuous phase transition, at which no latent heat involved in the course of transition and no co-existing phases [2,4]. A firm example of these is the phase transition experienced by PVT systems above the critical point [5]. The phenomena nearby critical point are known as critical phenomena, and affected by limited number of controlling variables such as the type of coupling interaction, symmetry of the microscopic constituents

Phase diagram of six-state clock model on rewired square lattices

2019

J. Phys.: Conf. Ser.

The six-state clock model (SSCM) on rewired square lattice is studied using Monte Carlo simulation with Wang-Landau algorithm. This is a discrete counterpart of the well-known XY model, the native host of a unique topological phase transition called Kosterlitz-Tholess (KT) transition. The model has two KT transitions, i.e., at temperature T 1 and T 2, where T 1 < T 2. The first transition separates the lower temperature magnetic order and the quasi-long range order (QLRO) also known as KT phase; while the second transition separates the QLRO and the higher temperature paramagnetic phase. It has been established that the presence of KT phase is affected by the presence of randomness in the form of site and bond dilution. This intermediate phase is totally ruled out if bonds or sites of the lattice are no longer percolated. Here different type of randomness is probed, namely the rewired lattices, obtained by randomly adding one extra bond to each lattice site, and connect the site to one of its next-nearest neighbors. As a results, the average number of neighbors C increases. The increase of C affects the existence of KT phase. For each value of C, the KT temperatures, T 1 and T 2, were estimated from the plot of specific heats. Variation of KT temperatures for different values of C is observed, which is plotted with respect to each corresponding C to obtain the system phase diagram.