Statistical Mechanics - Physics at Oregon State University

202 CHAPTER 9. GENERAL METHODS: CRITICAL EXPONENTS.
−0.996
−0.998
−1.0
−1.002
−1.004
0.9
0.95
Figure 9.2: Ideal case to find critical exponent.
−1.25
−1.275
−1.3
−1.325
−1.35
0.9
0.95
Figure 9.3: Non-analytic case to find critical exponent.
sample. Hence the procedure to find the critical exponents needs to consider
critical behavior close to the phase transition as a function of sample size. If
we replace the outside of the sample by something else, the values right at
the critical temperature change. For example, if we replace the outside by an
effective medium we obtain mean field results right at Tc. But away from the
critical temperature we get the characteristics of the sample, and the outside
world does not play a role. For a finite sample there are no singularities at the
phase transition, only smooth changes in behavior. If these changes become
abrupt for in the thermodynamic limit, then we have a singularity and a phase
transition.
x
1.0
x
1.0
1.05
1.05
1.1
1.1