InterJournal Complex Systems, 1661
Status: Accepted
Manuscript Number: [1661]
Submission Date: 2006
Precursors of a phase transition in a simple model system
Author(s): Vivian Halpern

Subject(s): CX.2



Most theoretical and numerical studies of phase transitions are concerned with the statistical mechanics and critical phenomena such as correlation lengths and critical slowing down as the temperature T is lowered towards the critical temperature Tc of the phase transition. However, an understanding of the microscopic properties of the system which are precursors of the phase transition as T approaches Tc is also of interest. Our studies show that the ferromagnetic 3-spin Potts models is a simple system in which these properties can readily be studied, and we have shown that changes in the environments of the states with time and temperature are responsible for its relaxation properties. Our new calculations indicate a change in the dominant relaxation mechanism as T approaches Tc, but not a dramatic change in them at Tc. On the other hand, we found that the tendency of the spins at most sites to return to their original values after having changed (which corresponds to the disapperance of long range diffusion of molecules in liquids as they freeze) does increase dramatically at Tc, so that the increase in this tendency as the temperature is lowered is a more reliable precursor of the phase transition. The relevance of these results to the behavior of other complex systems will be discussed.

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