scholarly journals A vanishing theorem for supersymmetric quantum field theory and finite size effects in multiphase cluster expansions

1991 ◽  
Vol 143 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Steven A. Janowsky ◽  
Jonathan Weitsman
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Size Effects ◽  
Finite Size ◽  
Quantum Field ◽  
Vanishing Theorem ◽  
Cluster Expansions ◽  
Finite Size Effects

Quantum field theory (QFT) at finite temperature: Equilibrium properties

2021 ◽  
pp. 786-830
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Phase Transitions ◽  
High Temperature ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Finite Size ◽  
Quantum Field ◽  
Statistical Field ◽  
Statistical Field Theory

Some equilibrium properties in statistical quantum field theory (QFT), that is, relativistic QFT at finite temperature are reviewed. Study of QFT at finite temperature is motivated by cosmological problems, high energy heavy ion collisions, and speculations about possible phase transitions, also searched for in numerical simulations. In particular, the situation of finite temperature phase transitions, or the limit of high temperature (an ultra-relativistic limit where the temperature is much larger than the physical masses of particles) are discussed. The concept of dimensional reduction emerges, in many cases, statistical properties of finite-temperature QFT in (1, d − 1) dimensions can be described by an effective classical statistical field theory in (d − 1) dimensions. Dimensional reduction generalizes a property already observed in the non-relativistic example of the Bose gas, and indicates that quantum effects are less important at high temperature. The corresponding technical tools are a mode-expansion of fields in the Euclidean time variable, singling out the zero modes of boson fields, followed by a local expansion of the resulting (d − 1)-dimensional effective field theory (EFT). Additional physical intuition about QFT at finite temperature in (1, d−1) dimensions can be gained by considering it as a classical statistical field theory in d dimensions, with finite size in one dimension. This identification makes an analysis of finite temperature QFT in terms of the renormalization group (RG), and the theory of finite-size effects of the classical theory, possible. These ideas are illustrated with several simple examples, the φ4 field theory, the non-linear σ-model, the Gross–Neveu model and some gauge theories.

scholarly journals SEMICLASSICAL METHODS IN 2D QFT: SPECTRA AND FINITE-SIZE EFFECTS

2006 ◽  
Vol 21 (28) ◽  
pp. 2099-2115 ◽  
Author(s):  
VALENTINA RIVA
Keyword(s):  
Size Effects ◽  
Finite Size ◽  
Large Mass ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Finite Size Effects ◽  
Small Coupling ◽  
Semiclassical Methods ◽  
Semiclassical Expansion

We review some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques, which generalize methods introduced during the '70s by Dashen, Hasllacher and Neveu and by Goldstone and Jackiw. The approach is best suited to deal with quantum field theories characterized by a nonlinear interaction potential with different degenerate minima, that generates kink excitations of large mass in the small coupling regime. Under these circumstances, although the results obtained are based on a small coupling assumption, they are nevertheless nonperturbative, since the kink backgrounds around which the semiclassical expansion is performed are nonperturbative too. We will discuss the efficacy of the semiclassical method as a tool to control analytically spectrum and finite-size effects in these theories.

scholarly journals Analytic theory of finite-size effects in supercell modeling of charged interfaces

2019 ◽  
Vol 21 (27) ◽  
pp. 14858-14864 ◽  
Author(s):  
Cong Pan ◽  
Shasha Yi ◽  
Zhonghan Hu
Keyword(s):  
Field Theory ◽  
Size Effects ◽  
Mean Field Theory ◽  
Mean Field ◽  
Finite Size ◽  
Analytic Theory ◽  
Finite Size Effects ◽  
Nonlinear Responses

Complex nonlinear responses of fluids to charge walls are predicted by mean-field theory.

scholarly journals Lattice φ4 Theory of Finite-Size Effects Above the Upper Critical Dimension

1998 ◽  
Vol 09 (07) ◽  
pp. 1073-1105 ◽  
Author(s):  
X. S. Chen ◽  
V. Dohm
Keyword(s):  
Field Theory ◽  
Lattice Model ◽  
Size Effects ◽  
Lattice Theory ◽  
Finite Size ◽  
Model Parameters ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Size Scaling

We present a perturbative calculation of finite-size effects near Tc of the φ4 lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ4 lattice theory and the φ4 field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At Tc, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to Tc of the lattice model, such as T max (L) of the maximum of the susceptibility χ, are found to scale asymptotically as Tc-T max (L) ~L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ max ~Ld/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to Tc have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d)/2 and L4-d terms predicted by our theory.

Field theory of finite-size effects in Ising-like systems

1995 ◽  
Vol 97 (2) ◽  
pp. 205-211 ◽  
Author(s):  
A. Esser ◽  
V. Dohm ◽  
M. Hermes ◽  
J. S. Wang
Keyword(s):  
Field Theory ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Effects

Quantum field theory at finite temperature

2019 ◽  
pp. 373-420
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Reduction ◽  
Finite Temperature ◽  
Finite Size ◽  
Heavy Ion ◽  
Effective Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Ion Collisions

Chapter 21 is devoted to quantum field theory at finite temperature, a topic that is relevant, for example, to high energy heavy ion collisions. Some similarity with finite size systems is pointed out with the relevance of zero modes. Finite temperature phase transitions are studied. An interesting issue concerns the conditions for dimensional reduction, that is, when can the initial field theory be replaced by an effective field theory without time dimension? The results of one–loop reduced action are presented. The solutions of RG equations are discussed. A few models with O(N) symmetry are investigated in the large N limit, which makes it possible to study directly crossover scale and the problem of dimensional crossover. The problem of dimensional reduction in Abelian gauge theories is examined.

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