A Theory of Cooperative Phenomena Export

@article{kikuchi-physical51, abstract = {A new method of approximation for order-disorder phenomena is developed. In Sec. A; the method is explained for the one-dimensional Ising lattice. Sections B and C cover the approximations already known; such as those of Bethe (Sec. B) and of Kramers-Wannier (Sec. C); which are shown to be derived as special cases of the method with suitable choices of variables. In Sec. D; an improved treatment is explained for the three-dimensional simple cubic Ising lattice. This approximation is found to agree with the rigorous expansion of the partition function up to the fourth moment by Kirkwood's moment method; so far as the disordered state is concerned. In Sec. E the general formula for the entropy is given. In Sec. H an improved treatment of the face-centered lattice (Ising model) is given.}, author = {Kikuchi, Ryoichi}, citeulike-article-id = {1243497}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.81.988}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v81/i6/p988_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v81/i6/p988_1}, day = {15}, doi = {10.1103/PhysRev.81.988}, journal = {Physical Review}, keywords = {gbp}, month = {March}, number = {6}, pages = {988+}, posted-at = {2008-12-03 08:41:24}, priority = {2}, publisher = {American Physical Society}, title = {A Theory of Cooperative Phenomena}, url = {http://dx.doi.org/10.1103/PhysRev.81.988}, volume = {81}, year = {1951} }

TY - JOUR ID - kikuchi-physical51 L3 - citeulike-article-id:1243497 N2 - A new method of approximation for order-disorder phenomena is developed. In Sec. A; the method is explained for the one-dimensional Ising lattice. Sections B and C cover the approximations already known; such as those of Bethe (Sec. B) and of Kramers-Wannier (Sec. C); which are shown to be derived as special cases of the method with suitable choices of variables. In Sec. D; an improved treatment is explained for the three-dimensional simple cubic Ising lattice. This approximation is found to agree with the rigorous expansion of the partition function up to the fourth moment by Kirkwood's moment method; so far as the disordered state is concerned. In Sec. E the general formula for the entropy is given. In Sec. H an improved treatment of the face-centered lattice (Ising model) is given. IS - 6 JF - Physical Review TI - A Theory of Cooperative Phenomena PB - American Physical Society VL - 81 SP - 988 KW - gbp AU - Kikuchi, Ryoichi PY - 1951/03/15/ UR - http://dx.doi.org/10.1103/PhysRev.81.988 ER -