%0 Journal Article %1 Burkhardt1976Application %A Burkhardt, Theodore W. %D 1976 %I American Physical Society %J Physical Review B %K blume-capel, renormalization, tricritical-points %N 3 %P 1196--1201 %R 10.1103/physrevb.14.1196 %T Application of Kadanoff's lower-bound renormalization transformation to the Blume-Capel model %U http://dx.doi.org/10.1103/physrevb.14.1196 %V 14 %X The critical behavior of the Blume-Capel model for d=2,3 is analyzed using a renormalization transformation based on Kadanoff's lower-bound transformation. There are fixed points associated with first-order, second-order, and tricritical phase transitions. The discontinuity fixed point onto which the line of first-order phase transition is mapped has two relevant eigenoperators with eigenvalue 2d, corresponding to the discontinuities in 〈σ〉 and 〈σ2〉. Quite different values of the variational parameters in the renormalization transformation optimize the free energy at each fixed point, making it difficult to calculate crossover behavior with the present approach.

@article{Burkhardt1976Application, abstract = {{The critical behavior of the Blume-Capel model for d=2,3 is analyzed using a renormalization transformation based on Kadanoff's lower-bound transformation. There are fixed points associated with first-order, second-order, and tricritical phase transitions. The discontinuity fixed point onto which the line of first-order phase transition is mapped has two relevant eigenoperators with eigenvalue 2d, corresponding to the discontinuities in 〈σ〉 and 〈σ2〉. Quite different values of the variational parameters in the renormalization transformation optimize the free energy at each fixed point, making it difficult to calculate crossover behavior with the present approach.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Burkhardt, Theodore W.}, biburl = {https://www.bibsonomy.org/bibtex/23e467f9cdcade54627f997538c517997/nonancourt}, citeulike-article-id = {9286341}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/physrevb.14.1196}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRB/v14/i3/p1196}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRB/v14/i3/p1196}, doi = {10.1103/physrevb.14.1196}, interhash = {25ea77cffa7d3a3e9711fcecc82f96ea}, intrahash = {3e467f9cdcade54627f997538c517997}, journal = {Physical Review B}, keywords = {blume-capel, renormalization, tricritical-points}, month = aug, number = 3, pages = {1196--1201}, posted-at = {2011-05-12 10:34:40}, priority = {2}, publisher = {American Physical Society}, timestamp = {2019-08-01T15:37:28.000+0200}, title = {{Application of Kadanoff's lower-bound renormalization transformation to the Blume-Capel model}}, url = {http://dx.doi.org/10.1103/physrevb.14.1196}, volume = 14, year = 1976 }