Tricritical swelling exponent in two dimensions estimations and exact values

1 Tricritical swelling exponent in two dimensions estimations and exact values 

For d — 3 the three-body interaction is just marginal. This is not the case for d 3 (and in particular for d = 2) since, then, the dimensionless parameter y = cS3 t becomes infinite when S - oo. In this case, a system with two-body and three-body interactions is tricritical when the second virial coefficient A2 vanishes (or z = 0). Then, for an isolated chain, the dependence of R2 with respect to S (for large S) is characterized by an exponent v, (v, 1/2) 

Just as Flory s exponent vF = 3j(d + 2) can be calculated from the equation 

The exponent v, has been estimated in a better way, by expanding v, in powers of e = 3 — d. In the framework of field theory, Stephen and McCauley17 calculated the exponents rjt = 2 — y,/v, and y, to order e2. For n = 0, their results are 

The value of v, for d = 2 has also been determined by computer simulation on lattices18,19 and, by using the strip method (see Chapter 12, Section 2.4), Derrida and Saleur19 found 

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