Critical Droplets and Phase Transitions in Two Dimensions

Details Critical Droplets and Phase Transitions in Two Dimensions Critical Droplets and Phase Transitions in Two Dimensions

2002-05-10

arxiv.org/abs/cond-mat/0205211v2

Phys.Rev. B67 (2003) 014102

Physics

Condensed Matter

Statistical Mechanics

Final version for publication, minor changes, figures added

Scientific paper

10.1103/PhysRevB.67.014102

In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability p_B<1, the corresponding site-bond clusters keep on percolating at T_c and the exponents do not change, until p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the critical percolation exponents switch to the 2D Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability p_c such that, for any p_B>=p_c, the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for p_c

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