24 July 2022 to 2 August 2022
House of International Conferences
Europe/Moscow timezone

Model A of critical dynamics: 5-loop ɛ expansion study

30 Jul 2022, 20:00
House of International Conferences

House of International Conferences

Dubna, Russia
Board: 19
Poster (portrait A1 or landscape A0) Young Scientist Forum Poster Session




The second order phase transitions and critical phenomena are accompanied by anomalous increase of correlation radius and relaxation time. On the approach of a system to its critical point, these values are described by power law and characterized by critical exponents. These universal constants depend on the dimension of the space and the number of components of the order parameter, but remain the same for all matter. The renormalization group method allows to obtain an asymptotic ε-expansion for the critical exponent, where ε=4-d is formally small parameter, which shows the deviation of the dimension of the space from its critical value dc=4.
We have calculated the five-loop RG expansions of the n-component A model of critical dynamics in dimensions d = 4−ε within the Minimal Subtraction scheme. This is made possible by using the advanced diagram reduction method and the Sector Decomposition technique adapted to the problems of critical dynamics. The ε expansions for the critical dynamic exponent z for an arbitrary value of the order parameter dimension n are derived. Based on these series, the numerical estimates of z for different universality classes are extracted and compared with the results obtained within different theoretical and experimental methods.
This work is focused on using resummation techniques for recently calculated 5-loop ε-expansion. For this purpose, Pade approximation and new modification of Borel resummation method proposed in were applied. Accounting the parameter which is in control of the asymptotics of the strong coupling along with the exact value of critical exponent for certain dimension [3] significantly increases result precision. However, both of these quantities are unknown for exponent z. The idea of the modification is to use the convergence criterion for determining optimal values of these parameters from the condition of the fastest convergence of the summation procedure.
Overall, obtained results demonstrate that account of new 5-loop term of ε-expansion for critical exponent z provides a rapprochement of RG estimations with other results of Monte-Carlo simulations.

Primary author



Prof. Loran Adzhemyan (Adzhemyan L.T.) Mr Daniel Evdokimov (Evdokimov D.A., )

Presentation Materials

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