Switching from a continuous to discontinuous phase transition under the quenched disorder

Abstract

Discontinuous phase transitions occurs to be particularly interesting from a social point of view because of their relationship to social hysteresis and critical mass. In this paper, we show that the replacement of a time-varying (annealed, situation-based) disorder by a static (quenched, personality-based) one can lead to a change from a continuous to a discontinuous phase transition. This is a result beyond the state of art, because so far numerous studies on various complex systems (physical, biological and social) have indicated that the quenched disorder can round or destroy the existence of a discontinuous phase transition. To show the possibility of the opposite behavior, we study a multistate $q$-voter model, with two types of disorder related to random competing interactions (conformity and anticonformity). We confirm, both analytically and through Monte Carlo simulations, that indeed discontinuous phase transitions can be induced by a static disorder.

arXiv commentMain text: 6 pages, 3 figures; Supplementary material: 6 pages, 4 figures

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Cited by in corpus (6)

• Polarization in the three-state $q$-voter model with anticonformity and bounded confidence
• Pair approximation for the q-voter models with quenched disorder on networks
• Thermal properties of structurally balanced systems on classical random graphs
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks
• Temperature-Noise Interplay in a Coupled Model of Opinion Dynamics
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order