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Center for Nonlinear Studies |
The phi^6 and asymmetric phi^4 models are commonly used to study first order phase transitions. We use the Smoluchowski equation to investigate the behavior of these model systems with inclusion of additive thermal noise, which smears a tricritical point into a “tricritical region”, and alters hysteresis effects. Many dynamical quantities can then be expressed as higher moments of the state distribution. We are particularly interested in tracking the behavior of the susceptibility of the state to an external field, an experimentally measurable quantity, in the tricritical region: while it diverges near critical points in deterministic models, we find that under noise it remains finite. This work is relevant to the study of materials such as Strontium Titanate, a quantum paraelectric material that may exhibit ferroelectric properties at low temperatures due to fluctuations.