Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation

The critical behavior of the two-dimensional N-vector cubic model is studied within the field-theoretical renormalization-group (RG) approach. The beta-functions and critical exponents are calculated in the five-loop approximation, RG series obtained are resummed using Pade-Borel-Leroy and conformal mapping techniques. It is found that for N = 2 the continuous line of fixed points is well reproduced by the resummed RG series and an account for the five-loop terms makes the lines of zeros of both beta-functions closer to each another. For N > 2 the five-loop contributions are shown to shift the cubic fixed point, given by the four-loop approximation, towards the Ising fixed point. This confirms the idea that the existence of the cubic fixed point in two dimensions under N > 2 is an artifact of the perturbative analysis. In the case N = 0 the results obtained are compatible with the conclusion that the impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure

Relaxational dynamics in 3D randomly diluted Ising models

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2).Comment: 38 page

Critical equation of state of randomly dilute Ising systems

We determine the critical equation of state of three-dimensional randomly dilute Ising systems, i.e. of the random-exchange Ising universality class. We first consider the small-magnetization expansion of the Helmholtz free energy in the high-temperature phase. Then, we apply a systematic approximation scheme of the equation of state in the whole critical regime, that is based on polynomial parametric representations matching the small-magnetization of the Helmholtz free energy and satisfying a global stationarity condition. These results allow us to estimate several universal amplitude ratios, such as the ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3) is in good agreement with experimental results on dilute uniaxial antiferromagnets.Comment: 21 pages, 1 figure, refs adde

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

Weak quenched disorder and criticality: resummation of asymptotic(?) series

In these lectures, we discuss the influence of weak quenched disorder on the critical behavior in condensed matter and give a brief review of available experimental and theoretical results as well as results of MC simulations of these phenomena. We concentrate on three cases: (i) uncorrelated random-site disorder, (ii) long-range-correlated random-site disorder, and (iii) random anisotropy. Today, the standard analytical description of critical behavior is given by renormalization group results refined by resummation of the perturbation theory series. The convergence properties of the series are unknown for most disordered models. The main object of these lectures is to discuss the peculiarities of the application of resummation techniques to perturbation theory series of disordered models.Comment: Lectures given at the Second International Pamporovo Workshop on Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001, Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files include

Randomly dilute spin models with cubic symmetry

We study the combined effect of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. For this purpose, we consider the field-theoretical approach based on the Ginzburg-Landau-Wilson $\phi^4$ Hamiltonian with cubic-symmetric quartic interactions and quenched randomness coupled to the local energy density. We compute the renormalization-group functions to six loops in the fixed-dimension (d=3) perturbative scheme. The analysis of such high-order series provides an accurate description of the renormalization-group flow. The results are also used to determine the critical behavior of three-dimensional antiferromagnetic three- and four-state Potts models in the presence of quenched impurities.Comment: 23 pages, 1 figure

Análise criminológica da proteção da integridade territorial da Ucrânia

Criminological analysis of the protection of the territorial integrity of Ukraine / Mykola Pakhnin, Andrii Nosach, Sergii Perepelytsia, Dariia Topal // DIXI. – 2022. – Vol. 24, № 2 (julio-diciembre). – P. 1-17. – DOI: https://doi.org/10.16925/2357-5891.2022.02.10Mykola Pakhnin, Andrii Nosach, Sergii Perepelytsia & Dariia Topal. Criminological analysis of the protection of the territorial integrity of Ukraine. DIXI, vol. 24, n°. 2, julio-diciembre 2022, 1-17. DOI: https://doi.org/10.16925/2357-5891.2022.02.10.Держава завжди унікальна у своїй діяльності та захисті, і для визнання кожної держави її цілісність завжди має поважатися — і ні за яких обставин не можна порушувати територіальну цілісність держави. З цією метою держава стає обов’язком забезпечити відповідне переслідування осіб, які злочинно посягають на територіальну цілісність. Навіть із запровадженням цього принципу територіальна цілісність держави завжди знаходиться під загрозою, що впливає на справжню сутність держави, яка полягає в захисті державного суверенітету. Ця стаття проголошує, що територіальна цілісність кожної держави повинна поважатися завжди, незалежно від обставин, а ті, хто її не поважає, повинні нести кримінальну відповідальність. У цьому питанні буде суть аналітичної методології дослідження, яка полягатиме у з’ясуванні кримінально-правового аспекту захисту територіальної цілісності України. З наведеної методології можна стверджувати, що відбуваються безперервні порушення територіальної цілісності України шляхом вчинення різноманітних злочинів. Саме тому потрібно щось робити у збереженні територіальної цілісності Держави Україна.The State is always unique in its activities and its protection, and for each State to be recognized, its integrity should always be respected — and under no circumstance the territorial integrity of a State should be tampered with. To this end, it becomes the responsibility of the State to ensure that those who criminally affect the territorial integrity should be prosecuted accordingly. Even with this principle put in place, the territorial integrity of the State is always threatened, thus affecting the real essence of the State being that of protecting State sovereignty. This article enunciates that the territorial integrity of every State should always be respected, regardless of the circumstances, and those who disrespect this should be criminally liable. In this question, there will be the essence of analytical research methodology, which will be to ascertain the criminal aspect of the protection of the territorial integrity of Ukraine. From the above methodology, one can say that there are continuous violations of the territorial integrity of Ukraine through the various crimes committed. It is for this reason that something needs to be done in preserving the territorial integrity of the State of Ukraine.Государство всегда уникально в своей деятельности и своей защите, и для того, чтобы каждое государство было признано, его целостность всегда должна уважаться, и ни при каких обстоятельствах нельзя посягать на территориальную целостность государства. С этой целью государство обязано обеспечить соответствующее судебное преследование тех, кто преступным образом затрагивает территориальную целостность. Даже при наличии этого принципа территориальная целостность государства всегда находится под угрозой, что затрагивает реальную сущность государства, заключающуюся в защите государственного суверенитета. В этой статье провозглашается, что территориальная целостность каждого государства всегда должна уважаться, независимо от обстоятельств, и те, кто нарушает это, должны нести уголовную ответственность. В этом вопросе будет суть методологии аналитического исследования, которая будет заключаться в констатации криминального аспекта защиты территориальной целостности Украины. Из приведенной методики можно сказать, что имеют место постоянные нарушения территориальной целостности Украины посредством совершения различных преступлений. Именно по этой причине необходимо что-то делать для сохранения территориальной целостности Государства Украина

Divergent Perturbation Series

Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov's method, according to which they are determined by the saddle-point configurations (instantons) of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series. Summing it, one can solve (in a certain approximation) various strong-coupling problems. This approach is demonstrated by determining the Gell-Mann - Low functions in \phi^4 theory, QED, and QCD for arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic forms are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical schemes for summation of perturbation series are described for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. High-order corrections to the Lipatov asymptotics are discussed.Comment: Review article, 45 pages, PD