Quantum and Thermal Fluctuations in the Ising Chains: A Case Study of Spin-Two System

For a system at absolute zero temperature, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a quantum phase transition (QPT) in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value. This paper presents a detailed and quantitative study of the magnetic properties of Ising two-spin system at zero temperature in the presence of longitudinal, transverse and mixed fields, and also at finite temperatures. At the critical longitudinal magnetic field, the system is found to undergo a QPT to a ferromagnetic state. For this system, an infinitesimal departure from zero transverse field is found to trigger off QPT and also remove the degeneracies that persisted even in the presence of longitudinal field. These quantum fluctuations, leading to QPT are more evident in the mixed field than the separate effect of longitudinal and transverse fields. The observed quantum effects at zero temperature for this system are found to be completely wiped out at finite temperatures due to thermal fluctuations. A temperature increase favours antiferromagnetic alignment of spins, while a decrease in temperature favours ferromagnetic alignment.