The crossover scaling behaviour for the lattice anisotropy of the susceptibility of the quasi-two-dimensional Ising models has been studied using high-temperature series expansions. The predictions of the extended scaling hypothesis are verified and the plots of the effective exponent are presented in the scaling regime. These results should provide a basis for comparison with experiments on quasi-two-dimensional Ising systems.

Journal of Physics C Solid State PhysicsJan 20, 19831 citation

Crossover of the dynamical behavior in two-dimensional random transverse Ising model

Shu-Xia Chen, Yin-Yang Shen, Xiang-Mu Kong

Physical Review BNov 3, 201025 citations

Journal of Magnetism and Magnetic Materials

Two-dimensional-to-one-dimensional crossover in the Ising model

Ichiro Hatta, Ryuzo Abe

Published Feb 1, 1983• 1 citation

Publisher

DOI: 10.1016/0304-8853(83)90814-4

Related papers

Size-driven dimensional crossover in the quasi-two-dimensional Ising model

Kyu Won Lee, Cheol Eui Lee

Solid State CommunicationsJan 13, 20041 citation

Dimensional crossover in the quasi-two-dimensional Ising-O(3) model

Naoki Kawashima, Yoshitomo Kamiya, Cristian D. Batista

Bulletin of the American Physical SocietyMar 1, 20120 citations

Crossover Critical Behavior in the Three-Dimensional Ising Model

Young C. Kim, Mikhail A. Anisimov, Jan V. Sengers +1 more

arXiv:cond-mat/0203190Journal of Statistical PhysicsMar 1, 200349 citations

Crossover anomalies in frustrated two-dimensional Ising spin system with four-spin interaction

J. Szṅajd

As is well known, one-dimensional spin systems with short-range interactions cannot undergo a phase transition at finite temperature. However, in many 1D Ising spin models with frustration, at a certain crossover point, the thermodynamic quantities show anomalies that resemble such a transition W. Yin [Phys. Rev. Res. 6, 013331 (2024)2643-156410.1103/PhysRevResearch.6.013331]. Recently, Yin [Phys. Rev. Res. 6, 013331 (2024)2643-156410.1103/PhysRevResearch.6.013331] has shown, using decorated ladders as an example, that a one-dimensional Ising model can be arbitrarily close to the genuine phase transition. Using the transfer matrix method and real space renormalization group technique, we find that crossover resembling a phase transition accompanied by gigantic specific heat can also occur in two-dimensional systems. We consider coupled Ising spin chains with a zig-zag structure and a four-spin j_{4} interaction, which allows us to control the temperature at which the spins become unbound in the model with short-range interactions. The crossover point is defined by two parameters: the crossover temperature t=t^{*} and the crossover interaction j_{4}=j_{4}^{*}, and occurs when the temperature at which the effective interaction between the spin subsystems zeros out coincides with the temperature at which the spins become unbound. In systems in which a genuine phase transition occurs at the critical temperature t=t_{c}, there are two possibilities: if t_{c}>t^{*} the system undergoes a sequence of three phase transitions with a reentrant transition to disordered phase, while for t_{c}<t^{*} the phase transition is preceded by the considered crossover. We study the key role in the appearance of anomalies in the thermodynamic quantities of the four-spin interactions which are suspected to have a significant impact on the properties of magnetic two-dimensional lattices, but possible also on the construction of social systems modeling the phenomenon of social validation or peer pressure.As is well known, one-dimensional spin systems with short-range interactions cannot undergo a phase transition at finite temperature. However, in many 1D Ising spin models with frustration, at a certain crossover point, the thermodynamic quantities show anomalies that resemble such a transition W. Yin [Phys. Rev. Res. 6, 013331 (2024)2643-156410.1103/PhysRevResearch.6.013331]. Recently, Yin [Phys. Rev. Res. 6, 013331 (2024)2643-156410.1103/PhysRevResearch.6.013331] has shown, using decorated ladders as an example, that a one-dimensional Ising model can be arbitrarily close to the genuine phase transition. Using the transfer matrix method and real space renormalization group technique, we find that crossover resembling a phase transition accompanied by gigantic specific heat can also occur in two-dimensional systems. We consider coupled Ising spin chains with a zig-zag structure and a four-spin j_{4} interaction, which allows us to control the temperature at which the spins become unbound in the model with short-range interactions. The crossover point is defined by two parameters: the crossover temperature t=t^{*} and the crossover interaction j_{4}=j_{4}^{*}, and occurs when the temperature at which the effective interaction between the spin subsystems zeros out coincides with the temperature at which the spins become unbound. In systems in which a genuine phase transition occurs at the critical temperature t=t_{c}, there are two possibilities: if t_{c}>t^{*} the system undergoes a sequence of three phase transitions with a reentrant transition to disordered phase, while for t_{c}<t^{*} the phase transition is preceded by the considered crossover. We study the key role in the appearance of anomalies in the thermodynamic quantities of the four-spin interactions which are suspected to have a significant impact on the properties of magnetic two-dimensional lattices, but possible also on the construction of social systems modeling the phenomenon of social validation or peer pressure.

Physical review. EFeb 13, 20254 citations

Crossover scaling function for the lattice anisotropy of the quasi-two-dimensional Ising models: the susceptibility

W.L. Basaiawmoit, S Singh

Journal of Physics C Solid State PhysicsJan 20, 19831 citation

Crossover of the dynamical behavior in two-dimensional random transverse Ising model

Shu-Xia Chen, Yin-Yang Shen, Xiang-Mu Kong

The dynamics of the two-dimensional spin- $\frac{1}{2}$ random transverse Ising model is studied by means of the recurrence relations method. Both the autocorrelation functions and the corresponding spectral densities are calculated in the cases that the exchange couplings or fields satisfy three typical distributions, respectively. For the cases of Gaussian and double-Gaussian distribution, when the standard deviation of the random variable is small, the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one, the result is similar to that of the bimodal distribution. While the standard deviation is large enough, the crossover disappears and the dynamics of the system shows a central-peak behavior or a disordered behavior.The dynamics of the two-dimensional spin-$\frac{1}{2}$ random transverse Ising model is studied by means of the recurrence relations method. Both the autocorrelation functions and the corresponding spectral densities are calculated in the cases that the exchange couplings or fields satisfy three typical distributions, respectively. For the cases of Gaussian and double-Gaussian distribution, when the standard deviation of the random variable is small, the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one, the result is similar to that of the bimodal distribution. While the standard deviation is large enough, the crossover disappears and the dynamics of the system shows a central-peak behavior or a disordered behavior.

Physical Review BNov 3, 201025 citations

The dynamics of the two-dimensional spin-

\frac{1}{2}

random transverse Ising model is studied by means of the recurrence relations method. Both the autocorrelation functions and the corresponding spectral densities are calculated in the cases that the exchange couplings or fields satisfy three typical distributions, respectively. For the cases of Gaussian and double-Gaussian distribution, when the standard deviation of the random variable is small, the dynamics of the system undergoes a crossover from a central-peak behavior to a collective-mode one, the result is similar to that of the bimodal distribution. While the standard deviation is large enough, the crossover disappears and the dynamics of the system shows a central-peak behavior or a disordered behavior.