The problem of critical behaviour of three dimensional random anisotropy magnets, which constitute a wide class of disordered magnets is considered. Previous results obtained in experiments, by Monte Carlo simulations and within different theoretical approaches give evidence for a second order phase transition for anisotropic distributions of the local anisotropy axes, while for the case of isotropic distribution such transition is absent. This outcome is described by renormalization group in its field theoretical variant on the basis of the random anisotropy model. Considerable attention is paid to the investigation of the effective critical behaviour which explains the observation of different behaviour in the same universality class.Comment: 41 pages, 10 figure

A functional renormalization group approach to d-dimensional, N -component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between d = 2.8 and d = 4 for various values of N focusing on the critical value, Nc(d), that, for a given dimension d, separates a first order region for N < Nc(d) from a second order region for N > Nc(d). Our approach concludes to the absence of stable fixed point in the physical -N = 2, 3 and d = 3 -cases, in agreement with ǫ = 4 − d-expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on conformal bootstrap program.

The ion-ion interactions become exponentially screened for ions confined in ultranarrow metallic pores. To study the phase behaviour of an assembly of such ions, called a superionic liquid, we develop a statistical theory formulated on bipartite lattices, which allows an analytical solution within the Bethe-lattice approach. Our solution predicts the existence of ordered and disordered phases in which ions form a crystal-like structure and a homogeneous mixture, respectively. The transition between these two phases can potentially be first or second order, depending on the ion diameter, degree of confinement and pore ionophobicity. We supplement our analytical results by three-dimensional off-lattice Monte Carlo simulations of an ionic liquid in slit nanopores. The simulations predict formation of ionic clusters and ordered snake-like patterns, leading to characteristic close-standing peaks in the cation-cation and anion-anion radial distribution functions.

We show that the critical behavior of two-and three-dimensional frustrated magnets cannot reliably be described from the known five-and six-loop perturbative renormalization-group results. Our conclusions are based on a careful reanalysis of the resummed perturbative series obtained within the zero-momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behavior strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O͑N͒ case, that there is apparent convergence of the critical exponents but toward erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z 2 topological defects in two-dimensional frustrated Heisenberg spins remains open.

We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as ∼ r −a . Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to twoloop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for 0.995 < a < 2 and is characterized by the correlation length exponent ν = 2/a + O ((2 − a) 3 ). Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent η2 = 1/2 − (2 − a)/4 + O ((2 − a) 2 ).

South Kensington Campus, London SW7 2AZ, United Kingdom ‡ 7 Interdisciplinary Scientific Center J-V Poncelet, UMI CNRS 2615, 11 Bol. Vlassievsky per., Moscow, Russia §We develop a theory of charge storage in ultra-narrow slit-like pores of nanostructured electrodes. Our analysis is based on the Blume-Capel model in external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterising the system, such as pore ionophilicity, interionic interaction energy and voltage. The phase diagram includes the lines of first and second-order, direct and re-entrant, phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. To test our predictions experimentally requires mono-disperse, conducting, ultra-narrow slit pores, permitting only one layer of ions, and thick pore walls, preventing interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and arXiv:1909.13089v1 [cond-mat.soft] 28 Sep 2019 ionophobic pores, and its underlying physics, may emerge in future experimental studies of more complex electrode structures.

We investigate the asymptotic and effective static and dynamic critical behavior of (d = 3)-dimensional magnets with quenched extended defects, correlated in ε d dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining d − ε d dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.

We study the conditions under which the critical behavior of the threedimensional mn-vector model does not belong to the spherically symmetrical universality class. In the calculations we rely on the field-theoretical renormalization group approach in different regularization schemes adjusted by resummation and extended analysis of the series for renormalization-group functions which are known for the model in high orders of perturbation theory. The phase diagram of the three-dimensional mn-vector model is built marking out domains in the mn-plane where the model belongs to a given universality class.PACS numbers: 05.50.+q, 64.60.Ak According to the universality hypothesis [1], asymptotic properties of the critical behavior remain unchanged for different physical systems if these are described by the same global parameters. The field-theoretical renormalization group (RG) approach [2] naturally takes into account the global parameters and derives properties of critical behavior from long distance properties of effective field theories. In