The dynamic phase transitions of periodically driven ferromagnets present a complex interplay between internal relaxation dynamics and external driving forces. In this study, a highly optimized Metropolis-Hastings Monte Carlo simulation is developed to model a two-dimensional Ising ferromagnet subjected to an oscillating magnetic field. Following exact thermodynamic validation of the static critical exponent of 1.75, the system is pushed out of equilibrium to investigate two competing mechanisms of phase disruption: structural spatial disorder and temporal frequency variation. Computational results demonstrate that quenched non-magnetic impurities act as localized pinning centers for expanding domain walls, fundamentally "softening" the material and drastically shrinking the dynamically ordered parameter space. Conversely, scaling the driving frequency outpaces localized spin relaxation, effectively bypassing the chaotic limit cycle and expanding the dynamically ordered phase. This dichotomy offers a comprehensive mathematical profile of non-equilibrium phase boundaries in disordered magnetic lattices.The dynamic phase transitions of periodically driven ferromagnets present a complex interplay between internal relaxation dynamics and external driving forces. In this study, a highly optimized Metropolis-Hastings Monte Carlo simulation is developed to model a two-dimensional Ising ferromagnet subjected to an oscillating magnetic field. Following exact thermodynamic validation of the static critical exponent of 1.75, the system is pushed out of equilibrium to investigate two competing mechanisms of phase disruption: structural spatial disorder and temporal frequency variation. Computational results demonstrate that quenched non-magnetic impurities act as localized pinning centers for expanding domain walls, fundamentally "softening" the material and drastically shrinking the dynamically ordered parameter space. Conversely, scaling the driving frequency outpaces localized spin relaxation, effectively bypassing the chaotic limit cycle and expanding the dynamically ordered phase. This dichotomy offers a comprehensive mathematical profile of non-equilibrium phase boundaries in disordered magnetic lattices.

Jun 1, 20260 citations

Models for Gapped Boundaries and Domain Walls

Alexei Kitaev, Liang Kong

arXiv:1104.5047Communications in Mathematical PhysicsJun 6, 2012443 citations

d_{x^2-y^2} Pair Domain Walls

Steven R. White, Douglas J. Scalapino

Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.Using the density matrix renormalization group, we study domain wall structures in the t-J model at a hole doping of x=1/8. We find that the domain walls are composed of d_{x^2-y^2} pairs and that the regions between the domain walls have antiferromagnetic correlations that are pi phase shifted across a domain wall. At x=1/8, the hole filling corresponds to one hole per two domain wall unit cells. When the pairs in a domain wall are pinned by an external field, the d_{x^2-y^2} pairing response is suppressed, but when the pinning is weakened, d_{x^2-y^2} pair-field correlations can develop.

arXiv:cond-mat/9610104Oct 13, 19960 citations

Pinning and Roughening of Domain Walls in Ising Systems Due to Random Impurities

David A. Huse, Christopher L. Henley

Randomly placed impurities that alter the local exchange couplings, but do not generate random fields or destroy the long-range order, roughen domain walls in Ising systems for dimensionality $\frac{5}{3}<d<5$ . They also pin (localize) the walls in energetically favorable positions. This drastically slows down the kinetics of ordering. The pinned domain wall is a new critical phenomenon governed by a zero-temperature fixed point. For $d=2$ , the critical exponents for domain-wall pinning energies and roughness as a function of length scale are estimated from numerically generated ground states.Randomly placed impurities that alter the local exchange couplings, but do not generate random fields or destroy the long-range order, roughen domain walls in Ising systems for dimensionality $\frac{5}{3}<d<5$. They also pin (localize) the walls in energetically favorable positions. This drastically slows down the kinetics of ordering. The pinned domain wall is a new critical phenomenon governed by a zero-temperature fixed point. For $d=2$, the critical exponents for domain-wall pinning energies and roughness as a function of length scale are estimated from numerically generated ground states.

Physical Review LettersJun 24, 1985766 citations

Phase transitions in two-dimensional model systems

William R. Schief

Jan 1, 19990 citations

Randomly placed impurities that alter the local exchange couplings, but do not generate random fields or destroy the long-range order, roughen domain walls in Ising systems for dimensionality

\frac{5}{3}<d<5

. They also pin (localize) the walls in energetically favorable positions. This drastically slows down the kinetics of ordering. The pinned domain wall is a new critical phenomenon governed by a zero-temperature fixed point. For

d=2

, the critical exponents for domain-wall pinning energies and roughness as a function of length scale are estimated from numerically generated ground states.