Abstract
An urgent problem in describing critical phenomena lies in the development of a generalizedtheory which allows one to obtain (except the calculation of critical exponents and some other uni-versal characteristics) explicit expressions for physical quantities like in the case of classic theories[1,2]. The scaling theory turns out to be the most developed with respect to this problem. It isbased on the similarity hypothesis proposed in [3{6] and on the scheme of constructing e ectiveKadano spin blocks [5]. We consider the system based on the Ising model on a simple cubic latticehaving a lattice constant c. The initial lattice is split into blocks with linear sizes s c, where sis an arbitrary number (s > 1). Then, instead of N initial sites with period c we get N
Highlights
An urgent problem in describing critical phenomena lies in the development of a generalized theory which allows one to obtain explicit expressions for physical quantities like in the case of classic theories [1,2]
When the system is near the phase transition point (PTP), the correlation length ξ is large and greatly exceeds C1
It turned out that it is possible to find an explicit form for the free energy using the results presented in [7,8,9,10,11]
Summary
An urgent problem in describing critical phenomena lies in the development of a generalized theory which allows one to obtain (except the calculation of critical exponents and some other universal characteristics) explicit expressions for physical quantities like in the case of classic theories [1,2]. At the presence of the external field (h = 0) with the temperature T tending to the critical point Tc, the presentation (10) is more appropriate since an arbitrary small field becomes essential (the quantity z tends to zero) In both cases of the RG transformation, this parameter (sτ or sh) exceeds the value of the correlation length. It turned out that it is possible to find an explicit form for the free energy using the results presented in [7,8,9,10,11] Such a calculation employs the collective variables (CV) set [12] and it is valid for arbitrary values of the field and temperature. Quantities xn and yn, which belong to the (3.4), are presented in (2.7)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
