Open AccessCritical exponents for the 3D Ising model
Author(s) -
Rajan Gupta,
Pablo Tamayo
Publication year - 1996
Language(s) - English
Resource type - Reports
DOI - 10.2172/251352
Subject(s) - ising model , scaling , exponent , statistical physics , monte carlo method , physics , renormalization group , critical exponent , approx , omega , renormalization , coupling (piping) , combinatorics , mathematics , mathematical physics , statistics , quantum mechanics , geometry , computer science , materials science , linguistics , philosophy , metallurgy , operating system
The authors present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 64{sup 3}, 128{sup 3}, and 256{sup 3} simple cubic lattices. Their MCRG estimates are K{sup c}{sub nn} = 0.221655(1)(1) and {nu} = 0.625(1). The FSS results for K{sup c} are consistent with those from MCRG but the value of {nu} is not. Their best estimate {eta} = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of their calculation is the estimate {omega} {approx} 0.7 for the correction-to-scaling exponent. The authors also present results for the renormalized coupling g{sub R} along the MCRG flow and argue that the data supports the validity of hyperscaling for the 3D Ising model