a Renormalization Group Study of Critical Phenomena in Three Dimensions.

Boundary critical phenomena are studied in the three-state Potts model in two dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and orbifold methods. Besides the previously known free, fixed and mixed boundary conditions a new one is obtained. This illustrates the necessity of considering fusion with operators that do not occur in the bulk spectrum, to obtain all boundary conditions. It is shown that this new boundary condition is dual to the mixed ones. The phase diagram for the quantum chain version of the Potts model is analysed using duality and renormalization group arguments.Boundary critical phenomena are studied in the three-state Potts model in two dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and orbifold methods. Besides the previously known free, fixed and mixed boundary conditions a new one is obtained. This illustrates the necessity of considering fusion with operators that do not occur in the bulk spectrum, to obtain all boundary conditions. It is shown that this new boundary condition is dual to the mixed ones. The phase diagram for the quantum chain version of the Potts model is analysed using duality and renormalization group arguments.

arXiv:cond-mat/9804117Journal of Physics A Mathematical and GeneralJul 17, 199873 citations

Boundary critical phenomena in the three-state Potts model

Ian K. Affleck, Masaki Oshikawa, Hubert Saleur

Nov 30, 200649 citations

Critical phenomena and the renormalization group

Franz Wegner

Springer eBooksApr 6, 20086 citations

Rethinking Dimensional Regularization in Critical Phenomena

P. Beretta, Alessandro Codello

We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$ -expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in $d=3$ under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.

arXiv:2604.25103Apr 28, 20260 citations

The renormalization group and critical phenomena

Kenneth Geddes Wilson

Reviews of Modern PhysicsJul 1, 19831,671 citations

We show that it is possible to use dimensional regularization (DR) beyond the usual

\varepsilon

-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG scheme - Functional Dimensional Regularization (FDR) - and apply it to a scalar theory in three dimensions. We compute the critical exponents of the Ising universality class directly in

d=3

under various typical approximations. The method that emerges combines the agility typical of DR with the generality proper of functional RG. Moreover, at a given order of approximation, FDR seems to provide faster convergence and better estimates than other functional RGs.