A method for obtaining critical properties of physical systems is presented. Based on a recursive relation involving a physical parameter of the system, it drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties. The method is illustrated for several ferromagnetic Ising systems on well-known Bravais lattices. A finite-size scaling approach is performed, by applying the method on lattices of different sizes. The efficiency of the method is confirmed by evaluating critical temperatures, as well as critical exponents, that turn up to be in good agreement with those available in the literature, with a relatively small computational effort.A method for obtaining critical properties of physical systems is presented. Based on a recursive relation involving a physical parameter of the system, it drives the system spontaneously to the critical point, providing an efficient way to estimate critical properties. The method is illustrated for several ferromagnetic Ising systems on well-known Bravais lattices. A finite-size scaling approach is performed, by applying the method on lattices of different sizes. The efficiency of the method is confirmed by evaluating critical temperatures, as well as critical exponents, that turn up to be in good agreement with those available in the literature, with a relatively small computational effort.

Brazilian Journal of PhysicsJun 1, 20029 citations

Critical Dynamics in Simple Ising-Like Systems

Gene F. Mazenko

Springer series in solid-state sciencesJan 1, 19830 citations

Numerical Studies of Critical Points of the Long-range Transverse-field Ising Chain

Xinyang Shen

The criticality of the ferromagnetic long-range transverse-field Ising chain (LRTFIC) with periodic boundary conditions and power-law decaying Ising coupling is studied using the Density Matrix Renormalization Group (DMRG). The ground states of the systems at different values of the transverse field $h$ are obtained using DMRG. From these ground states, a quantity called crosscap overlap can be extracted efficiently. This thesis suggests that the crosscap overlap can serve as an indicator to identify the critical points of the LRTFIC. The estimated critical points are further verified by data collapse. For the decay exponent $\alpha=3.5$ , the LRTFIC belongs to the short-range regime. DMRG is performed on systems with different sizes up to $N=280$ . The critical point is estimated to be $h_c \approx 1.25$ , at which the crosscap overlaps approach the exact value of the short-range Ising chain as the system size grows.The criticality of the ferromagnetic long-range transverse-field Ising chain (LRTFIC) with periodic boundary conditions and power-law decaying Ising coupling is studied using the Density Matrix Renormalization Group (DMRG). The ground states of the systems at different values of the transverse field $h$ are obtained using DMRG. From these ground states, a quantity called crosscap overlap can be extracted efficiently. This thesis suggests that the crosscap overlap can serve as an indicator to identify the critical points of the LRTFIC. The estimated critical points are further verified by data collapse. For the decay exponent $\alpha=3.5$, the LRTFIC belongs to the short-range regime. DMRG is performed on systems with different sizes up to $N=280$. The critical point is estimated to be $h_c \approx 1.25$, at which the crosscap overlaps approach the exact value of the short-range Ising chain as the system size grows.

Jan 1, 20260 citations

Critical exponents of Ising-like systems in general dimensions

Yurij V. Holovatch

Theoretical and Mathematical PhysicsSep 1, 199317 citations

Clusters and Critical Behavior in the Ising Model

Jean-Luc Cambier

Jan 1, 19850 citations

Lee–Yang-zero Ratio Method in Three-dimensional Ising Model

Tatsuya Wada, Masakiyo Kitazawa, K. Kanaya

By performing Monte Carlo simulations of the three-dimensional Ising model, we apply the recently proposed Lee-Yang-zero ratio (LYZR) method to determine the location of the critical point in this model. We demonstrate that the LYZR method is as powerful as the conventional Binder-cumulant method in studying the critical point, while the LYZR method has the advantage of suppressing the violation of the finite-size scaling and non-linearity near the critical point. We also achieve a precise determination of the values of the LYZRs at the critical point, which are universal numbers. In addition, we propose an alternative method that uses only a single Lee-Yang zero and show that it is also useful for the search for the critical point.By performing Monte Carlo simulations of the three-dimensional Ising model, we apply the recently proposed Lee-Yang-zero ratio (LYZR) method to determine the location of the critical point in this model. We demonstrate that the LYZR method is as powerful as the conventional Binder-cumulant method in studying the critical point, while the LYZR method has the advantage of suppressing the violation of the finite-size scaling and non-linearity near the critical point. We also achieve a precise determination of the values of the LYZRs at the critical point, which are universal numbers. In addition, we propose an alternative method that uses only a single Lee-Yang zero and show that it is also useful for the search for the critical point.

arXiv:2508.20422Journal of the Physical Society of JapanJan 20, 20263 citations

h

are obtained using DMRG. From these ground states, a quantity called crosscap overlap can be extracted efficiently. This thesis suggests that the crosscap overlap can serve as an indicator to identify the critical points of the LRTFIC. The estimated critical points are further verified by data collapse. For the decay exponent

\alpha=3.5

, the LRTFIC belongs to the short-range regime. DMRG is performed on systems with different sizes up to

N=280

. The critical point is estimated to be

h_c \approx 1.25

, at which the crosscap overlaps approach the exact value of the short-range Ising chain as the system size grows.