Probability distributions of the order ...
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Title :
Probability distributions of the order parameter of the $O(N)$ model
Author(s) :
Rançon, Adam [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Delamotte, Bertrand [Auteur]
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]
Šaravanja, Lovro [Auteur]
Balog, Ivan [Auteur]

Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Delamotte, Bertrand [Auteur]
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]
Šaravanja, Lovro [Auteur]
Balog, Ivan [Auteur]
HAL domain(s) :
Physique [physics]/Matière Condensée [cond-mat]
English abstract : [en]
We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O(N)$ model at criticality using the functional renormalisation group. For this purpose, we generalize the method ...
Show more >We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O(N)$ model at criticality using the functional renormalisation group. For this purpose, we generalize the method introduced in [Balog et al., Phys. Rev. Lett. {\bf 129}, 210602 (2022)] to the $O(N)$ model. We study the large $N$ limit, as well as the cases $N=2$ and $N=3$ at the level of the Local Potential Approximation (LPA), and compare our results to Monte Carlo simulations. We compute the entire family of universal scaling functions, obtained in the limit where the system size $L$ and the correlation length of the infinite system $\xi_\infty$ diverge, with the ratio $\zeta=L/\xi_\infty$ constant. We also generalize our results to the approach of criticality from the low-temperature phase where another infinite family of universal PDF exists. We find that the LPA describes very well the functional form of the family of PDFs, once we correct for a global amplitude of the (logarithm of the) PDF and of $\zeta$.Show less >
Show more >We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O(N)$ model at criticality using the functional renormalisation group. For this purpose, we generalize the method introduced in [Balog et al., Phys. Rev. Lett. {\bf 129}, 210602 (2022)] to the $O(N)$ model. We study the large $N$ limit, as well as the cases $N=2$ and $N=3$ at the level of the Local Potential Approximation (LPA), and compare our results to Monte Carlo simulations. We compute the entire family of universal scaling functions, obtained in the limit where the system size $L$ and the correlation length of the infinite system $\xi_\infty$ diverge, with the ratio $\zeta=L/\xi_\infty$ constant. We also generalize our results to the approach of criticality from the low-temperature phase where another infinite family of universal PDF exists. We find that the LPA describes very well the functional form of the family of PDFs, once we correct for a global amplitude of the (logarithm of the) PDF and of $\zeta$.Show less >
Language :
Anglais
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Submission date :
2025-01-23T04:28:21Z
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