One-loop Effective Potential in Higher-dimensional Yang-Mills Theory

We study the effective action in Euclidean Yang-Mills theory with a compact simple gauge group in one-loop approximation assuming a covariantly constant gauge field strength as a background. For groups of higher rank and spacetimes of higher dimensions such field configurations have many independent color components taking values in Cartan subalgebra and many “magnetic fields” in each color component. In our previous investigation it was shown that such background is stable in dimensions higher than four provided the amplitudes of “magnetic fields” do not differ much from each other. In the present paper we exactly calculate the relevant zeta-functions in the case of equal amplitudes of “magnetic fields”. For two “magnetic fields” with equal amplitudes the behavior of the effective action is studied in detail. It is shown that in dimensions d = 4,5,6,7 (8), the perturbative vacuum is metastable, i.e., it is stable in perturbation theory but the effective action is not bounded from below, whereas in dimensions d = 9,10,11 (8) the perturbative vacuum is absolutely stable. In dimensions d = 8 (8) the perturbative vacuum is stable for small values of the coupling constant but becomes unstable for large coupling constant leading to the formation of a non-perturbative stable vacuum with nonvanishing “magnetic fields”. The critical value of the coupling constant and the amplitudes of the vacuum “magnetic fields” are evaluated exactly. PACS numbers: 11.10Kk, 11.15Tk, 11.15.-q, 12.38Aw, 12.38Lg     

Phase Transitions in a Mixture of Hard-Sphere Dipoles and Neutral Hard Spheres

Using the reference hypernetted chain （RHNC） integral equation theory and a rigorous stability analysis method, we investigate the phase behavior of a mixture of hard-sphere dipoles and neutral hard spheres based on the correlations of the homogeneous isotropic phase. Lowering the temperature down to the points where the RHNC equations fail to have a solution, several ttuctuations strongly increase. At low densities our results indicate the onset of ／ chain formation, which is similar with the pure DHS system. At high densities, the results indicate the appearance of isotropic-to-ferroelectric transitions （small neutral hard spheres concentrations） and demixing transitions （large neutral hard spheres concentrations）.     

Phase Transitions in a Mixture of Hard-Sphere Dipoles and Neutral Hard Spheres

Using the reference hypernetted chain (RHNC) integral equation theory and a rigorous stability analysis method, we investigate the phase behavior of a mixture of hard-sphere dipoles and neutral hard spheres based on the correlations of the homogeneous isotropic phase. Lowering the temperature down to the points where the RHNC equations fail to have a solution, several fluctuations strongly increase. At low densities our results indicate the onset of chain formation, which is similar with the pure DHS system. At highdensities, the results indicate the appearance of isotropic-to-ferroelectric transitions (small neutral hard spheres concentrations) and demixing transitions (large neutral hard spheres concentrations).     

Structural Stability Theory and Phase Transitions Models

Global stability theory is introduced as a tool allowing the classification of mathematical models of phase transitions. The point of view is that a topological structure whose stability controls the transition, can be identified in the process of computation of the partition function. In particular we discuss mean field theories and the two dimensional Ising model. Interesting features are disclosed concerning the classification of the instabilities, such as the number of parameters and possible approximations.     

Diffusion and Velocity Correlations of the Phase Transitions in a System of Macroscopic Rolling Spheres

We study an air-fluidized granular monolayer composed of plastic spheres which roll on a metallic grid. The air current is adjusted so that the spheres never lose contact with the grid and so that the dynamics may be regarded as pseudo two dimensional (or two dimensional, if the effects of the sphere rolling are not taken into account). We find two surprising continuous transitions, both of them displaying two coexisting phases. Moreover, in all the cases, we found the coexisting phases display a strong energy non-equipartition. In the first transition, at a weak fluidization, a glass phase coexists with a disordered fluid-like phase. In the second transition, a hexagonal crystal coexists with the fluid phase. We analyze, for these two-phase systems, the specific diffusive properties of each phase, as well as the velocity correlations. Surprisingly, we find a glass phase at a very low packing fraction and for a wide range of granular temperatures. Both phases are also characterized by strong anticorrelated velocities upon a collision. Thus, the dynamics observed for this quasi two-dimensional system unveil phase transitions with peculiar properties, very different from the predicted behavior in well-know theories for their equilibrium counterparts.     

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.     

Effective Lagrangian of SU（2） Yang—Mills Theory in the Presence of Fermions

We derive the one-loop effective action of SU(2) Yang-Mills theory in the presence of fermions in the low energy limit.This result is presented by separating the topological degrees,which describe the non-Abelian monopoles from the dynamical degrees of the gauge potential and integrate out all the dynamical degrees and fermions in SU(2) Yang-Mills theory.     

Extended Connection in Yang-Mills Theory

The three fundamental geometric components of Yang-Mills theory –gauge field, gauge fixing and ghost field– are unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to generalize the notion of gauge fixing by using a gauge fixing connection instead of a section. From the equations for the extended connection’s curvature, we derive the relevant BRST transformations without imposing the usual horizontality conditions. We show that the gauge field’s standard BRST transformation is only valid in a local trivialization and we obtain the corresponding global generalization. By using the Faddeev-Popov method, we apply the generalized gauge fixing to the path integral quantization of Yang-Mills theory. We show that the proposed gauge fixing can be used even in the presence of a Gribov’s obstruction.     

Phase Transitions in Tungsten Monoborides

JETP Letters - Three tungsten monoboride phases, including the I41/amd-WB and Cmcm-WB phases and the recently predicted stable low-temperature $$Poverline 4 {2_1}m$$-WB phase, have been studied in...     

Phase Transitions in Layered Systems

We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\) , called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\) , where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\) , where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.     

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.     

Magnetic Phase Transitions in CePtSn

CePtSn, crystallizing in the orthorhombic TiNiSi-type structure, exhibits two antiferromagnetic transitions at T _N=7.8 K and T _M=5.2 K. Low-temperature X-ray diffraction study has been done to investigate changes in lattice parameters connected with these magnetic phase transitions. Specific-heat data in the same temperature region are also presented. Magnetization isotherms at T>T _N up to 14 T have been measured and the obtained results are compared with theoretical calculations based on a microscopic model Hamiltonian.     

Modified Yang-Mills Theory and Electroweak Interactions

Since the Higgs boson of the standard electroweak model has not been detecteddespite many experimental attempts, nonstandard electroweak models notincluding the Higgs boson may be worthy of consideration; one of them isproposed here. This new model of electroweak interactions is based on theYang-Mills theory completed by a nontrivial condition at infinity for theYang-Mills potentials corresponding to the zero-field intensities. It is shown thatwithin the framework of this model the three vector potentials of the Yang-Millstheory allow one to describe both the Maxwell electromagnetic interactions andthe Fermi weak interactions and to obtain the known value of the Z ⁰ boson mass.     

Critical Points and Phase Transitions

Journal of Experimental and Theoretical Physics - Various critical phenomena and critical points appearing in many-particle systems under the variation of external conditions (fields), including...     

Notes on Black Hole Phase Transitions

In these notes we present a summary of existing ideas about phase transitions of black hole spacetimes in semiclassical gravity and offer some thoughts on three possible scenarios or mechanisms by which these transitions could take place. We begin with a review of the thermodynamics of a black hole system and emphasize that the phase transition is driven by the large entropy of the black hole horizon. Our first theme is illustrated by a quantum atomic black hole system, generalizing to finite-temperature a model originally offered by Bekenstein. In this equilibrium atomic model, the black hole phase transition is realized as the abrupt excitation of a high energy state, suggesting analogies with the study of two-level atoms. Our second theme argues that the black hole system shares similarities with the defect-mediated Kosterlitz–Thouless transition in condensed matter. These similarities suggest that the black hole phase transition may be more fully understood by focusing upon the dynamics of black holes and white holes, the spacetime analogy of vortex and antivortex topological defects. Finally, we compare the black hole phase transition to another transition driven by an (exponentially) increasing density of states, the Hagedorn transition first found in hadron physics in the context of dual models or the old string theory. In modern string theory the Hagedorn transition is linked by the Maldacena conjecture to the Hawking–Page black hole phase transition in Anti-de Sitter (AdS) space, as observed by Witten. Thus, the dynamics of the Hagedorn transition may yield insight into the dynamics of the black hole phase transition. We argue that characteristics of the Hagedorn transition are already contained within the dynamics of classical string systems. Our third theme points to carrying out a full nonperturbative and nonequilibrium analysis of the large N behavior of classical SU(N) gauge theories to understand its Hagadorn transition. By invoking the Maldacena conjecture we can then gain valuable insight into black hole phase transitions in AdS space.     

用独立元格等效作用量研究三维U(1)格点规范理论的相结构

在格点规范理论中,应用变分累积展开方法,引入独立元格等效作用量,研究了三维U(1)格点规范理论的元格内能,得到连续的内能曲线,与Monte Carlo(MC)数据相符,表明理论是禁闭的.     

Decoherence and Phase Transitions in Quantum Dynamics

A particle with internal degrees of freedom is in contact with a bath of photons (necessitating a relativistic treatment). The occurrence of decoherence is established and the density matrix is found to be diagonal in momentum space. In the case of non-trivial internal degrees of freedom and selection rules there is a first order phase transition separating those degrees of freedom. Finally, because probability amplitudes become probabilities, Einstein’s proposal that more than one detector could respond to a signal is answered.

     

Magnetic Phase Transitions in Nanoclusters and Nanostructures

New phenomena – the first order magnetic phase transitions were observed in nanoclusters and nanostructures. For isolated ferrihydrite nanoclusters (d ～ 1–2 nm) in porous materials, for α-,γ-Fe₂O₃ nanoclusters (d ～ 20–50 nm) and for composites of nanostructured metallic Eu with additives of α-, γ-Fe₂O₃ nanoclusters and adamantane the critical temperatures (T _C, T _N) and magnetic cluster critical sizes (R _cr) were determined by means of thermodynamic models and Mössbauer spectroscopy. The first order magnetic phase transitions (jump-like) proceed by such a way when magnetization and magnetic order disappear by jump without superparamagnetic relaxation. According to thermodynamic model predictions the cluster and interface defects were suggested to play the main role in magnetic behavior. Thus, for the defective α-, γ-Fe₂O₃ nanoclusters, at R ≤ R _cr, the presence of the first order (jump-like) magnetic phase transition was described in terms of magnetic critical size of cluster. The action of high pressure (up to 2 GPa) with shear (120–240°) was effective for defect generation and nanostructure formation. For nanosystems including iron oxide nanoclusters, adamantane and metallic europium and subjected to shear stress under high pressure loading the critical value of defect density was estimated by the study of the character of magnetic phase transition. First-to-second-order (nanostructured metallic Eu) and second-to-first-order (α-, γ-ferric oxide nanoclusters) changes of the character of magnetic phase transition were shown to accompany by the variation of critical temperatures compared to the corresponding bulk values.     

Partition Function Zeros at First-Order Phase Transitions: Pirogov—Sinai Theory

This paper is a continuation of our previous analysis(2) of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of ref. 2 were established are satisfied by a large class of lattice models. These models are characterized by two basic properties: The existence of only a finite number of ground states and the availability of an appropriate contour representation. This setting includes, for instance, the Ising, Potts, and Blume–Capel models at low temperatures. The combined results of ref. 2 and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class.