In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.In this paper we propose an Ising model on an infinite ladder lattice, which is made of two infinite Ising spin chains with interactions. It is essentially a quasi-one-dimessional Ising model because the length of the ladder lattice is infinite, while its width is finite. We investigate the phase transition and dynamic behavior of Ising model on this quasi-one-dimessional system. We use the generalized transfer matrix method to investigate the phase transition of the system. It is found that there is no nonzero temperature phase transition in this system. At the same time, we are interested in Glauber dynamics. Based on that, we obtain the time evolution of the local spin magnetization by exactly solving a set of master equations.

Communications in Theoretical PhysicsSep 1, 20071 citation

Simulations on Infinite-Size Lattices

Hans Gerd Evertz, Wolfgang von der Linden

We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. All two-point functions can be obtained, including dynamical information. When the number of iterations is increased, correlation functions at larger distances become available. Limits $q\ensuremath{\rightarrow}0$ and $\ensuremath{\omega}\ensuremath{\rightarrow}0$ can be approached directly. As examples we calculate spectra for the $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ Ising model and for Heisenberg quantum spin ladders with two and four legs.We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at $\ensuremath{\beta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. All two-point functions can be obtained, including dynamical information. When the number of iterations is increased, correlation functions at larger distances become available. Limits $q\ensuremath{\rightarrow}0$ and $\ensuremath{\omega}\ensuremath{\rightarrow}0$ can be approached directly. As examples we calculate spectra for the $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ Ising model and for Heisenberg quantum spin ladders with two and four legs.

arXiv:cond-mat/0008072Physical Review LettersMay 28, 200115 citations

Dopant pairing in a disordered magnetic spin ladder

K. Knakkergaard Nielsen

I demonstrate a pairing mechanism of dopants in a magnetic lattice, emerging from the underlying of the spins. The effect is demonstrated in a mixed-dimensional model, where dopants travel along a two-leg ladder, while the spins feature Ising interactions along the rungs and the legs of the ladder. The dynamics following the sudden immersion of two nearest neighbor dopants in an infinite temperature spin lattice shows that thermal spin disorder frustrates the relative motion of the dopants and enforces them to copropagate. The predictions are shown to be realistically testable in quantum simulation experiments.I demonstrate a pairing mechanism of dopants in a magnetic lattice, emerging from the underlying of the spins. The effect is demonstrated in a mixed-dimensional model, where dopants travel along a two-leg ladder, while the spins feature Ising interactions along the rungs and the legs of the ladder. The dynamics following the sudden immersion of two nearest neighbor dopants in an infinite temperature spin lattice shows that thermal spin disorder frustrates the relative motion of the dopants and enforces them to copropagate. The predictions are shown to be realistically testable in quantum simulation experiments.

arXiv:2407.01252Physical Review ResearchFeb 12, 20251 citation

d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2

Ising model and for Heisenberg quantum spin ladders with two and four legs.