On the critical behavior of the spin-s Ising model

Abstract

The spin-s one dimensional Ising model is studied analytically within the framework of transfer matrix method. Exact results for some thermodynamical properties such as the internal energy, the entropy, the magnetization and the magnetic susceptibility are obtained for general spin-s in the absence (presence) of a magnetic field. The critical behavior of the thermodynamical properties are analysed for some values of spin-s (1/2, 1 and 3/2) at different temperature and field. The asymptotic behavior of these properties are investigated especially close to the critical temperature T → 0 and when T → ∞.

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

“…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].…”

“…Ostilli and Mukhamedov [31] determined the free energy by deriving the transfer matrix for a 1D three-state Potts model in the presence of a q-component external field. However, under certain special circumstances, calculations were performed in the absence of the q-component external field (see [29,35] for more information). It is worth noting that in section 3, for non-zero external field, obtaining the transfer matrix, we will specifically develop the transfer matrix by assuming the external magnetic field variable to be zero as applications.…”

“…Within the framework of thermodynamic characteristics, it is commonly recognized that the average spin value offers significant details about the system's macroscopic behavior [29,30]. Representing the overall magnetic behavior, it is a measure of the predicted or average orientation of spins in the ensemble.…”

“…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].…”

“…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]. Taking into account the Hamiltonian provided by equation (2.1) and in the presence of an external magnetic field, the expression for the canonical partition function for this system can be formulated as follows:…”