Development And Change in the Social Fabric: A Statistical Mechanical Analysis Using Quantum Phase Transition and LMG Model

We have analyzed here the changing pattern of social order of an agricultural community during the transition period, when an industrial unit is being built up at that locality for a certain period of time, on the basis of a statistical model. We have mapped here the situation onto the phase transition in the Lipkin-Meshkov-Glick (LMG) model induced by a quench, the quench time being identified with the target time for the completion of the project. To map the system as a spin model we consider each individual as a spin. We take that an individual having independent profession and those having professions dependent on others correspond to up and down spin states. During the transition when people having independent profession of cultivation are forced to take odd jobs and become dependent on others, we associate this with a spin flip which occurs during phase transition of the LMG model. Indeed when phase transition is induced by a quench, we have defect formation causing spins to be flipped and the density of defects related to the fraction of flipped spins depends on the quench time.