Abstract In the previous chapters we have dedicated ample space to the study of two-dimensional statistical systems at criticality, providing their exact solutions in terms of conformal field theories. In this chapter we start investigating the deformations of conformal field theories that move the statistical systems away from criticality. As pointed out in Chapter 8, in the renormalization group approach the characterization of the universality classes must include, in addition to the conformal theory of the fixed points, also the description of the scaling region nearby.Abstract In the previous chapters we have dedicated ample space to the study of two-dimensional statistical systems at criticality, providing their exact solutions in terms of conformal field theories. In this chapter we start investigating the deformations of conformal field theories that move the statistical systems away from criticality. As pointed out in Chapter 8, in the renormalization group approach the characterization of the universality classes must include, in addition to the conformal theory of the fixed points, also the description of the scaling region nearby.

Aug 27, 20090 citations

Critical phenomena and scale invariance

Franz Wegner

Springer eBooksDec 11, 20055 citations

Conformal Gaussian Approximation

Anı́bal Iucci, Carlos Naón

We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative prediction of conformal invariance, valid for systems in the scaling regime, away from criticality. We illustrate our idea by considering, as an example, the sine-Gordon model. Our method gives a good approximation for the soliton mass as function of $β$ .We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative prediction of conformal invariance, valid for systems in the scaling regime, away from criticality. We illustrate our idea by considering, as an example, the sine-Gordon model. Our method gives a good approximation for the soliton mass as function of $β$.

arXiv:hep-th/0109118Sep 14, 20011 citation

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