Monte Carlo and renormalization group local effective potentials in scalar field theories at finite temperature

1997 ◽  
Vol 55 (8) ◽  
pp. 4990-4996 ◽  
Author(s):  
J. D. Shafer ◽  
J. R. Shepard
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Scalar Field ◽  
Finite Temperature ◽  
Field Theories ◽  
Effective Potentials

scholarly journals Monte Carlo and renormalization-group effective potentials in scalar field theories

1995 ◽  
Vol 51 (12) ◽  
pp. 7017-7025 ◽  
Author(s):  
J. R. Shepard ◽  
V. Dmitrašinović ◽  
J. A. McNeil
Keyword(s):  
Monte Carlo ◽  
Renormalization Group ◽  
Scalar Field ◽  
Field Theories ◽  
Effective Potentials

SCHWINGER α-PARAMETRIC REPRESENTATION OF FINITE TEMPERATURE FIELD THEORIES: RENORMALIZATION

1990 ◽  
Vol 05 (23) ◽  
pp. 4427-4440 ◽  
Author(s):  
M. BENHAMOU ◽  
A. KASSOU-OU-ALI
Keyword(s):  
Temperature Field ◽  
Scalar Field ◽  
Finite Temperature ◽  
Short Range ◽  
Parametric Representation ◽  
Field Theories ◽  
Compact Form ◽  
Zero Temperature ◽  
Feynman Amplitudes ◽  
Temperature Scalar

We present the extension of the zero temperature Schwinger α-representation to the finite temperature scalar field theories. We give, in a compact form, the α-integrand of Feynman amplitudes of these theories. Using this representation, we analyze short-range divergences, and recover in a simple way the known result that the counterterms are temperature-independent.

RG IMPROVEMENT OF THE EFFECTIVE POTENTIAL AT FINITE TEMPERATURE

1996 ◽  
Vol 11 (28) ◽  
pp. 2259-2269 ◽  
Author(s):  
HISAO NAKKAGAWA ◽  
HIROSHI YOKOTA
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Finite Temperature ◽  
Renormalization Group Equation ◽  
Effective Procedure ◽  
Coefficient Function ◽  
Group Equation ◽  
Leading Order ◽  
Effective Potentials ◽  
The One

We present a simple and effective procedure to improve the finite temperature effective potential so as to satisfy the renormalization group equation (RGE). With the L-loop knowledge of the effective potential and of the RGE coefficient function, this procedure carries out a systematic resummation of large-T as well as large-log terms up to the Lth-to-leading order, giving an improved effective potential which satisfies the RGE and is exact up to the Lth-to-leading T and log terms. Applications to the one- and two-loop effective potentials are explicitly performed.

scholarly journals Multicritical hypercubic models

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
R. Ben Alì Zinati ◽  
A. Codello ◽  
O. Zanusso
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Fixed Points ◽  
Point Group ◽  
Field Theories ◽  
Invariant Polynomials ◽  
Entire Family ◽  
Spin Models ◽  
Single Spin ◽  
Special Cases

Abstract We study renormalization group multicritical fixed points in the ϵ-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group HN. After reviewing the algebra of HN-invariant polynomials and arguing that there can be an entire family of multicritical (hyper)cubic solutions with ϕ2n interactions in $$ d=\frac{2n}{n-1}-\epsilon $$ d = 2 n n − 1 − ϵ dimensions, we use the general multicomponent beta functionals formalism to study the special cases d = 3 − ϵ and $$ d=\frac{8}{3}-\epsilon $$ d = 8 3 − ϵ , deriving explicitly the beta functions describing the flow of three- and four-critical (hyper)cubic models. We perform a study of their fixed points, critical exponents and quadratic deformations for various values of N, including the limit N = 0, that was reported in another paper in relation to the randomly diluted single-spin models, and an analysis of the large N limit, which turns out to be particularly interesting since it depends on the specific multicriticality. We see that, in general, the continuation in N of the random solutions is different from the continuation coming from large-N, and only the latter interpolates with the physically interesting cases of low-N such as N = 3. Finally, we also include an analysis of a theory with quintic interactions in $$ d=\frac{10}{3}-\epsilon $$ d = 10 3 − ϵ and, for completeness, the NNLO computations in d = 4 − ϵ.

Renormalization group study of scalar field theories

1986 ◽  
Vol 270 ◽  
pp. 687-701 ◽  
Author(s):  
Anna Hasenfratz ◽  
Peter Hasenfratz
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Field Theories

scholarly journals Renormalization of scalar field theories in rational spacetime dimensions

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
J. A. Gracey
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Field Theories ◽  
Critical Dimensions ◽  
Group Functions

Abstract We renormalize various scalar field theories with a $$\phi ^n$$ϕn self interaction such as $$n=5$$n=5, 7 and 9 in their respective critical dimensions which are non-integer. The renormalization group functions for the O(N) symmetric extensions are also computed.

UNIFIED TREATMENT OF THE SCALAR FIELD THEORIES-Φn THROUGH THOMPSON'S RENORMALIZATION GROUP METHOD

2003 ◽  
Vol 17 (26) ◽  
pp. 4645-4660 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Present Method ◽  
Critical Dimension ◽  
Energy Scale ◽  
Field Theories ◽  
Group Method ◽  
Renormalization Group Method ◽  
Coupling Constant ◽  
Upper Critical Dimension

In this work we apply Thompson's scaling approach (of dimensions) to study the scalar field theories Φn. This method can be considered as a simple and alternative way to the renormalization group (RG) approach and when applied to the Φn Lagrangian is able to obtain the coupling constant behavior g(μ), namely the dependence of g on the energy scale μ. The calculations are evaluated just at [Formula: see text], where the dimension dc is similar to a kind of upper critical dimension of the problem, or in other words the dimension where the Φn theory becomes renormalizable, so that we obtain logarithmic behavior of the coupling g at dc. Due to the universal logharithmic behavior of the coupling g at dc for any value of n in the Φn theory, we are able to estimate a certain βn function given in a closed form, which is a novelty obtained by the present method.

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