Phase transitions of ?extended? Ising models on a square lattice

Рамазанов Магомедшейх Курбанович, Akai Kurbanovich Murtazaev, М. А. Магомедов

H Ulman, M Athematics J Ournal

Seung‐Yeon Kim

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.

Valeriy A Ryabov

J. Rosenfeld, N.E. Ligterink

The phase transition present in the linear-chain and square-lattice cases of the transverse Ising model is examined. The extended coupled-cluster method (ECCM) can describe both sides of the phase transition with a unified approach. The correlation length and the excitation energy are determined. The ECCM is able to use both the weak- and the strong-coupling starting states within a calculation based on the same uncorrelated model state.

Yu-Liang Xu, Xiang-Mu Kong, Zhongqiang Liu +1 more