Electronic Resource
Springer
Journal of statistical physics
58 (1990), S. 599-615
ISSN:
1572-9613
Keywords:
Statistical mechanics
;
Potts models
;
algebraic functions
;
transfer matrix
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A method of using algebraic curves to obtain estimates of critical points accurate enough to identify them as simple algebraic numbers (if that is what they are) is discussed and illustrated with an application to the (q-state Potts model on the triangular lattice for cases of pure two-site interactions and pure three-site interactions. In the latter case the critical point is conjectured to be $$z_c^2 = (\tfrac{1}{2}\sqrt 3 )^{(q - 2)/2} + q(q \geqslant )$$ . In a similar conjecture for the critical percolation probability on thedirected square lattice,q c 1/2 (q c +3)=2(q c +p c =1).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01112765
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