2001-10-31
10:15 at ML H43

Relationship between Small System Thermodynamics and Finite-Size Scaling

Thomas Petermann

Institute of Polymers, ETH

My talk will be devoted to the relevant problem of establishing a connection between Hill's small system thermodynamics and the theory of critical phenomena extended to finite systems, i.e. finite-size scaling. Using renormalization group considerations, the finite-size scaling form of the free energy per degree of freedom is put on a firm basis. An expression for a quantity describing the deviation from the macroscopic limit is found, this establishes the desired relationship on an abstract level. Numerically computed finite-size scaling functions lead to a more specific ansatz for the free energy. This permits the derivation of a power-law between the quantity which describes the deviation from the macroscopic limit and the system size with an appropriate exponent. This result is regarded as new, and it confirms that the thermodynamics of small systems consistently applies to critical phenomena.