Diverging correlation length

Flere we discuss only briefly the simulation of continuous transitions (see [132. 135] and references therein). Suppose that tire transition is characterized by a non-vanishing order parameter X and a corresponding divergent correlation length We shall be interested in the block average value where the L... 

Now, assume that we are getting closer to the critical point of our transition, i.e., to the point of the second-order transition. In the case of a uniform system the critical region can be described by the divergent correlation length of statistical fluctuations [138]... 

Ising model harbors a critical point. It can be shown (see [bax82]) that the correlation length = [ln(Ai/A2)] h If H = 0, however, then it can also be shown that limy g+(Ai/Aj) = 1 and, thus, that oo at // = 7 = 0. Since one commonly associates a divergent correlation length with criticality, it is in this sen.se that 7/ = T = 0 may be thought of as a critical point. 

In three dimensions, 9 = 2v l.26 and Ra = (To Q flk Tc=0. i9. Not only are the scaling relations (7.67) and (7.68) obtained from the simplified model in agreement with RG theory, the estimated value of the amplitude ratio R 0.39 is close to the universal theoretical value 7 o = 0-37. This value is confirmed by the most reliable experiments on fluids. Relationships between other thermodynamic properties and the diverging correlation length can be obtained in a similar fashion. 

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