Frustrations and orderings in Ising chain with multiple interactions

Abstract

We study the frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice, taking into account the exchange interactions of atomic spins at the sites of the nearest, next-nearest, and third neighbors. The exact analytical expressions for the thermodynamic functions of the system are obtained using the Kramers-Wannier transfer matrix technique. Criteria for the emergence of magnetic frustrations in the presence of competition between the energies of exchange interactions are formulated. The points and intervals of the existence of frustrations, which depend on the values and signs of the exchange interactions, are found. The features of the entropy and heat capacity of this model in the frustration regime and its vicinity are investigated. Non-zero entropy values of the ground state of a frustrated system, as well as a two-peak temperature structure of the heat capacity in the vicinity of the frustration point, are found. at the sites of the nearest, second, and third neighbors (J 1 < 0, J 2 < 0, J 3 < 0), the lines emerging from the point (31) defining the boundaries of the spin configurations C A4 , C A6 and C A2 are given byfor regions C A4 and C A6 with the energy of states at the boundary E = J 2 , and alsofor the boundary between the configurations C A6 and C A2 with the energy E = J 3 . In the ferro-antiferro-ferromagnetic variant of the exchange interaction parameters (J 1 > 0, J 2 < 0, J 3 > 0), the lines emerging from the point (31) defining the boundaries of the spin configurations C A4 , C A3 and C F2 are given by the expressions

Frustrations on decorated planar lattices in Ising model

“…Note that this situation does not contradict the third law of thermodynamics [43] and was thoroughly discussed in Refs. [49,50].…”

The Investigation of a Temperature and Field Characteristics of the One-dimensional Ising Model with Competing Exchange Interactions

“…Низкоразмерные магнитные системы привлекают к себе внимание ученых достаточно давно [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Модель Изинга имеет точное решение в одномерном и двумерном случае.…”