The Continuous-Spin, Ising Model of Field Theory and the Renormalization Group

1980 ◽  
pp. 91-114
Author(s):  
George A. Baker
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Ising Model ◽  
Continuous Spin

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

STOCHASTIC FIELD THEORY AND RENORMALIZATION GROUP APPROACH TO CRITICAL BEHAVIORS IN THERMO FIELD DYNAMICS

1989 ◽  
Vol 04 (09) ◽  
pp. 2185-2210
Author(s):  
B. BHATTACHARYA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Finite Temperature ◽  
Internal Field ◽  
Point Of View ◽  
Internal Space ◽  
Theoretic Approach ◽  
Stochastic Field ◽  
Stochastic Fields ◽  
Renormalization Group Approach

We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.

Limitations on universality in the continuous-spin Ising model

1984 ◽  
Vol 17 (5) ◽  
pp. L275-L278 ◽  
Author(s):  
G A Baker ◽  
J D Johnson
Keyword(s):  
Ising Model ◽  
Continuous Spin

Continuous-Spin Ising Model andλ:ϕ4:dField Theory

1979 ◽  
Vol 42 (22) ◽  
pp. 1431-1434 ◽  
Author(s):  
George A. Baker ◽  
John M. Kincaid
Keyword(s):  
Ising Model ◽  
Continuous Spin
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