ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Two repellent particles are bound to occupy two among thek n +1 adjacent sites 0=x 0 (n) 〈x 1 (n) 〈...〈x kn (n) =1, sayx q (n) ,x q+1 (n) . Define the Hamiltonian ℋ q (n) =−ln(x q+1 (n) −x q (n) ) and the partition function We discuss the behaviour of the function $$F(\beta ) = \mathop {\lim \sup }\limits_{n \to + \infty } \frac{{\ln Z(\beta , n)}}{{\ln k_n }},$$ closely related to the free energy. We prove that the smallest real zero ofF(β) is equal to the fractal dimension of the system and that this number, when less than one, is a critical value whereF is not analytic.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02102110
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