Calculation of Thermodynamic Quantities of 1D Ising Model with Mixed Spin-(s,(2t − 1)/2) by Means of Transfer Matrix

Abstract

In this paper, we consider the one-dimensional Ising model (shortly, 1D-MSIM) having mixed spin-(s,(2t−1)/2) with the nearest neighbors and the external magnetic field. We establish the partition function of the model using the transfer matrix. We compute certain thermodynamic quantities for the 1D-MSIM. We find some precise formulas to determine the model’s free energy, entropy, magnetization, and susceptibility. By examining the iterative equations associated with the model, we use the cavity approach to investigate the phase transition problem. We numerically determine the model’s periodicity.

The qualitative properties of 1D mixed-type Potts-SOS model with 1-spin and its dynamical behavior

“…It may be written as the total of all conceivable states, each of which is weighted by the Boltzmann factor e − β H [36]. The subsequent procedure involves employing the bond representation and breaking down the Boltzmann weights into pairwise factors, essentially decomposing the bonds [16,36]. So, we get We define σ N+1 to be equal to σ 1 in order to establish periodic boundary conditions (see [30] for details).…”

“…So, we get We define σ N+1 to be equal to σ 1 in order to establish periodic boundary conditions (see [30] for details). Therefore, from (A2) we obtain the partition function as Now, it is feasible to define the entire thermodynamic properties of the model by utilizing either the partition function and the finite-size free energy or one of its derived forms [16,29,30,35]. From (A4), we obtain the free energy associated with the model as Many researchers have examined other thermodynamic properties as a result of derivatives of the free energy function provided in (A5) with regard to certain parameters [16,29,30,35].…”

“…Using the Kramers-Wannier transfer technique, which requires building a transfer matrix and determining its eigenvalues, we can solve the problem [16,29,35]. The matrix transfer approach is widely employed in statistical mechanics due to its broad range of applications, making it one of the most frequently utilized methods [29][30][31].…”