Petar Mali

Phase diagram of spin-12 quantum Heisenberg J1–J2 antiferromagnet on the body-centered-cubic lattice in random phase approximation

Abstract Magnetic properties of spin 1 2 J 1 – J 2 Heisenberg antiferromagnet on the body centered cubic lattice are investigated. By using two-time temperature Greens functions, sublattice magnetization and critical temperature depending on the frustration ratio p = J 2 / J 1 are obtained in both stripe and Neel phases. The analysis of ground state sublattice magnetization and phase diagram indicates the critical end point at J 2 / J 1 = 0.714 , in agreement with previous studies.

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

Abstract Dynamics of driven dissipative Frenkel–Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middleton’s no passing rule.

Farey sequence in the appearance of subharmonic Shapiro steps.

The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model

The devils staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Multipath Metropolis simulation: An application to the classical Heisenberg model

This study explores the Multipath Metropolis simulation of the classical Heisenberg model. Unlike the standard single-path algorithm, the Metropolis algorithm applied to multiple random-walk paths becomes an embarrassingly parallel algorithm in which many processor cores can be easily utilized. This is important since processor cores are progressively becoming less expensive and thus more accessible. The most obvious advantage of the multipath approach is in employing independent random-walk paths to produce an uncorrelated simulation output with a normal distribution allowing for straightforward and rigorous statistical analysis.

Shapiro steps in the commensurate structures with integer value of the winding number

Abstract Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate structures with integer values of winding number in the dc- and ac-driven overdamped Frenkel-Kontorova model. While in the standard case with sinusoidal substrate potential, the system reduces to the single particles model in which only harmonic steps exist and analytical form for the step size can be revealed, in the case of deformable potential, the presence of many degrees of freedom strongly influences the Shapiro steps. Whole series of subharmonic steps appear, and the two types of response functions, the one for the commensurate structures with odd and the one for the commensurate structures with even winding number have been observed.