1996/04/30 by Sen-Ben Liao, Michael Strickland · 27 citations
Earth and Planetary Sciences · Physics and Astronomy · #Black Holes and Theoretical Physics #Constant (computer programming) #Critical exponent #Crossover #High-pressure geophysics and materials #Phase transition #Polynomial #Renormalization #Renormalization group #Scale (ratio) #Scaling #Theoretical and Computational Physics #cond-mat #hep-th
paper · pdf · doi:10.1016/s0550-3213(97)00212-5
published in Nuclear Physics B 497(3), 611-638 (Elsevier BV) · 24 pages, TeX, 8 figures in separate file, Updated version to appear in Nucl. Phys. B
arxiv created 1997/04/07 · openalex publication_date 1997/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate the critical behavior of the lambda phi4 theory defined on S1 x Rd having two finite length scales beta, the circumference of S1, and k-1, the blocking scale introduced by the renormalization group transformation. By numerically solving the coupled differential RG equations for the finite-temperature blocked potential Ubeta,k(Phi) and the wavefunction renormalization constant Zbeta,k(Phi), we demonstrate how the finite-size scaling variable betabar = beta k determines whether the phase transition is (d+1)- or d-dimensional in the limits betabar >> 1 and betabar << 1, respectively. For the intermediate values of betabar, finite-size effects play an important role. We also discuss the failure of the polynomial expansion of the effective potential near criticality.