What Differentiates Crossovers from Phase Transitions in Thermodynamics?

[andlessa]

Hi,

Could anyone point me to a reference (textbook, review article...) with a clear explanation of the physics of crossovers? My main interest is to understand it in a microscopical level or in terms of a phenomenological effective potential a la second order phase transitions. I'd like to understand under what conditions a theory moves from a phase transition to a crossover.
Sorry for such a basic question, but I've always had a very poor knowledge of thermodynamics.

Thanks

 

[TheDestroyer]

I think Schwabl - Statistical mechanics has a good chapter about phase transitions :)

 

[sir-pinski]

for your question about crossovers and phase transitions. Crossovers and phase transitions are both important concepts in the field of thermodynamics and can be understood in terms of changes in the physical properties of a system. However, they are distinct phenomena and have different underlying mechanisms.

A phase transition is a sudden and sharp change in the physical properties of a system, such as its density, magnetization, or heat capacity, as a result of a change in external conditions like temperature or pressure. Phase transitions can be classified into different types, such as first-order, second-order, or higher-order transitions, depending on the discontinuity in the physical properties at the transition point.

On the other hand, a crossover is a smooth and gradual change in the physical properties of a system as a result of varying external conditions. Crossovers can occur when there is no clear boundary between two phases, and the physical properties of the system continuously change without any abrupt jump.

In terms of a microscopic level or an effective potential, phase transitions can be described by a discontinuity in the potential, while crossovers can be described by a smooth change in the potential. This means that the energy landscape of the system changes abruptly at a phase transition, while it changes gradually at a crossover.

The conditions for a theory to exhibit a phase transition or a crossover depend on the specific system and its interactions. Generally, phase transitions occur when there is a competition between different energy states, and one state becomes energetically favored over the other as external conditions change. Crossovers, on the other hand, occur when the energy landscape is continuously changing, and there is no clear energy minimum.

I recommend looking into textbooks or review articles on statistical mechanics or thermodynamics for a more detailed explanation of crossovers and phase transitions. Some good references include "Introduction to Modern Statistical Mechanics" by David Chandler and "Thermodynamics and Statistical Mechanics" by Walter Greiner. I hope this helps clarify the concept of crossovers and phase transitions for you.