Ising spin ladder with trimer rungs and next-nearest-neighbor coupling. Frustration in physics and agent models

TL;DR

This paper investigates a complex Ising spin ladder model with trimer rungs and next-nearest-neighbor interactions, revealing sharp phase crossovers driven by frustration, with implications for understanding abrupt social opinion changes.

Contribution

It introduces an extended Ising ladder model with asymmetric interactions and NNN couplings, analyzing phase crossovers using transfer matrix and renormalization group methods.

Findings

Identifies frustration-driven sharp phase crossovers in the model.

Shows crossover points coincide with vanishing effective interleg coupling.

Proposes social opinion shifts can be modeled as phase crossovers without true phase transitions.

Abstract

The extended model of two-leg Ising spin ladder with trimer rungs and next nearest neighbor interaction (NNN) in an external magnetic field is studied using the transfer matrix and linear renormalization group methods. In the standard version (with the same only NN interactions in both legs) such a ladder exhibits very interesting behavior - a frustration driven extremely sharp phase crossover at finite temperature which resembles a phase transition, impossible in one dimension. It is shown that in all considered cases with different interactions in each leg (assymetric ladder), with NNN interactions and in the presence of small external field such a crossover takes place when the point at which the effective interleg coupling vanishes coincides with the point at which the interleg correlation function exhibits an inflection point accompanied by the specific heat maximum. A hypothesis is formulated that to describe an abrupt change in political view of the people it is not necessary to resort to a concept of a phase transition, controversial for social systems. In some cases, this phenomenon can be understood as a phase crossover triggered by the level of frustration. The source of this frustration is proposed as an internal conflict between two areas of attitudes of the society members, personal and economic, which are shaped by personality traits possibly modified by life experience.