ترغب بنشر مسار تعليمي؟ اضغط هنا

Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations

419   0   0.0 ( 0 )
 نشر من قبل Hugh Osborn
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its extension, the derivative expansion. The results are compared with the epsilon expansion by showing that the non linear differential equations may be linearised at each multicritical point and the epsilon expansion treated as a perturbative expansion. The results for critical exponents are compared with corresponding epsilon expansion results from standard perturbation theory. The results provide a test for the validity of the local potential approximation and also the derivative expansion. An alternative truncation of the exact RG equation leads to equations which are similar to those found in the derivative expansion but which gives correct results for critical exponents to order $epsilon$ and also for the field anomalous dimension to order $epsilon^2$. An exact marginal operator for the full RG equations is also constructed.



قيم البحث

اقرأ أيضاً

180 - J. Berges , G. Hoffmeister 2008
Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description . For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium.
We outline a separable matrix ansatz for the potentials in effective field theories of nonrelativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation for these po tentials. New fixed points indicate a much richer structure than previously recognized in the RG flows of simple short-range potentials.
211 - Boris Krippa 2005
The application of the exact renormalisation group to a many-fermion system with a short-range attractive force is studied. We assume a simple ansatz for the effective action with effective bosons, describing pairing effects and derive a set of appro ximate flow equations for the effective coupling including boson and fermionic fluctuations. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The mean-field results are recovered if boson-loop effects are omitted. The calculations with two different forms of the regulator was shown to lead to similar results.
We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs quartic coupling , as well as its non-minimal coupling to gravity and Newtons constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented.
129 - Tom Steudtner 2020
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $overline{text{MS}}$ scheme. Utilising pre-exis ting literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and derive $beta$ functions for scalar masses and cubic interactions from it. As an example, the results are applied to compute all renormalisation group equations in $U(n) times U(n)$ scalar theories.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا