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Continuous freezing in an infinite-range one-dimensional model.

Carlo Carraro¹

¹Department of Chemical Engineering, University of California, Berkeley, California 94720, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 6, 2003

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This study evaluates the partition function for a one-dimensional hard rod fluid with long-range interactions. It reveals conditions for condensation or a continuous freezing transition in the infinite range limit.

Area of Science:

Statistical Mechanics
Condensed Matter Physics

Background:

Classical one-dimensional hard rod fluid models are fundamental in statistical mechanics.
Understanding phase transitions, such as condensation and freezing, is crucial in condensed matter physics.

Purpose of the Study:

To exactly evaluate the partition function of a classical one-dimensional hard rod fluid with residual long-range interactions.
To investigate the conditions leading to condensation or freezing transitions in the infinite range limit.

Main Methods:

Utilizing an auxiliary field to evaluate the partition function.
Analyzing the Fourier spectrum of the residual interaction potential.
Considering the limit where the interaction range extends to infinity.

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Main Results:

In the infinite range limit, the system recovers the Kac-Uhlenbeck-Hemmer model of condensation if the residual interaction's Fourier spectrum lacks finite wave vector components.
If the Fourier spectrum contains finite wave vector components, a continuous second-order freezing transition is predicted.

Conclusions:

The nature of the phase transition (condensation vs. freezing) is determined by the spectral properties of the residual interaction at infinite range.
This work provides an exact analytical framework for studying phase transitions in one-dimensional systems with long-range interactions.