We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interactions, since such a system is physically realized in the insulator $\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}$ . The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.We investigate roughening transitions in the context of transverse-field Ising models. As a modification of the transverse Ising model with short range interactions, which has been shown to exhibit domain wall roughening, we have looked into the possibility of a roughening transition for the case of long-range interactions, since such a system is physically realized in the insulator $\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}$. The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.

arXiv:cond-mat/0505002Physical Review BAug 5, 20056 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 the Ising model with transverse field

James R. Kirkwood

Journal of Statistical PhysicsNov 1, 19844 citations

Roughening Dynamics of Interfaces in the Two-Dimensional Quantum Ising Model

Wladislaw Krinitsin, Niklas Tausendpfund, Matteo Rizzi +2 more

The properties of interfaces are key to understanding the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale tree tensor network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.The properties of interfaces are key to understanding the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale tree tensor network simulations to identify the dynamical signature of an interface roughening transition within the ferromagnetic phase of the 2D quantum Ising model. For initial domain wall profiles we find extended prethermal plateaus for smooth interfaces, whereas above the roughening transition the domain wall decays quickly. Our results can be readily explored experimentally in Rydberg atomic systems.

arXiv:2412.10145Physical Review LettersMay 21, 20258 citations

Properties of the phase transitions in the transverse Ising model

L. De Cesare, Ileana Rabuffo, Dimo I. Uzunov

Jan 1, 19980 citations

\mathrm{Li}\mathrm{Ho}{\mathrm{F}}_{4}

. The combination of strong Ising anisotropy and long-range forces lead naturally to the formation of domain walls but we find that the long-range forces destroy the roughening transition.

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.