Finite-temperature Transition Research Articles

Dynamical ac study of the critical behavior in Heisenberg spin glasses

We present some numerical results for the Heisenberg spin-glass model with Gaussian interactions, in a three dimensional cubic lattice. We measure the AC susceptibility as a function of temperature and determine an apparent finite temperature transition which is compatible with the chiral-glass temperature transition for this model. The relaxation time diverges like a power law $\tau\sim (T-T_c)^{-z\nu}$ with $T_c=0.19(4)$ and $z\nu=5.0(5)$. Although our data indicates that the spin-glass transition occurs at the same temperature as the chiral glass transition, we cannot exclude the possibility of a chiral-spin coupling scenario for the lowest frequencies investigated.

Spontaneous interlayer coherence in bilayer Kondo systems

Bilayer Kondo systems present interesting models to illustrate the competition between the Kondo effect and intermoment exchange. Such bilayers can exhibit two sharply distinct Fermi liquid phases which are distinguished by whether or not the local moments participate in the Fermi sea. We study these phases and the evolution from one to the other upon changing Kondo coupling. We argue that an ordered state with spontaneous interlayer phase coherence generically intervenes between the two Fermi liquids. Such a condensate phase breaks a U(1) symmetry and is bounded by a finite-temperature Kosterlitz-Thouless transition. Based on general arguments and mean-field calculations we investigate the phase diagram and associated quantum phase transitions.

Critical or tricritical point in mixed-action [formula omitted] lattice gauge theory?

An analysis of scaling along the first-order bulk transition line in fundamental-adjoint SU ( 2 ) lattice gauge theory strongly supports the first-order endpoint being a tricritical point, and is inconsistent with it being an ordinary critical point as is usually assumed. If tricritical, the transition must continue from the endpoint further into the phase diagram as a second-order bulk transition and extend to and beyond the Wilson axis. Observations indicate that this is most likely the same transition that has been traditionally considered a finite-temperature transition.

The finite-temperature chiral transition in QCD with adjoint fermions

We study the nature of the finite-temperature chiral transition in QCD with N_f light quarks in the adjoint representation (aQCD). Renormalization-group arguments show that the transition can be continuous if a stable fixed point exists in the renormalization-group flow of the corresponding three-dimensional Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by exploiting two three-dimensional perturbative approaches, the massless minimal-subtraction scheme without epsilon expansion and a massive scheme in which correlation functions are renormalized at zero momentum. We compute the renormalization-group functions in the two schemes to five and six loops respectively, and determine their large-order behavior. The analyses of the series show the presence of a stable three-dimensional fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This fixed point does not appear in an epsilon-expansion analysis and therefore does not exist close to four dimensions. The finite-temperature chiral transition in two-flavor aQCD can therefore be continuous; in this case its critical behavior is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may show a more complex phase diagram with two phase transitions. One of them, if continuous, should belong to the O(3) vector universality class.

Observable signature of the Berezinskii–Kosterlitz–Thouless transition in a planar lattice of Bose–Einstein condensates

We investigate the possibility that Bose–Einstein condensates, loaded on a 2D optical lattice, undergo—at finite temperature—a Berezinskii–Kosterlitz–Thouless transition. We show that—in an experimentally attainable range of parameters—a planar lattice of Bose–Einstein condensates is described by the XY model at finite temperature. We demonstrate that the interference pattern of the expanding condensates provides the experimental signature of the Berezinskii–Kosterlitz–Thouless transition by showing that, near the critical temperature, the component of the momentum distribution and the central peak of the atomic density profile sharply decrease. The finite-temperature transition for a 3D optical lattice is also discussed in this paper, and analogies with superconducting Josephson junction networks are stressed throughout the text.

The finite temperature transition for 3-flavour lattice QCD at finite isospin density

We simulate 3-flavour lattice QCD with a small chemical potential $\mu_I$ for isospin, at temperatures close to the finite temperature transition. Using quark masses just above the critical mass for zero chemical potential, we determine the position of the transition from hadronic matter to a quark-gluon plasma as a function of $\mu_I$. We see evidence for a critical endpoint where the transition changes from a crossover to a first-order transition as $\mu_I$ is increased. We argue that QCD at finite $\mu_I$ and QCD at finite quark-numberchemical potential $\mu$ should behave similarly in this region.

N-ality and topology at finite temperature

We study [JHEP 0309 (2003) 034] the spectrum of confining strings in SU(3) pure gauge theory, in different representations of the gauge group. Our results provide direct evidence that the string spectrum agrees with predictions based on n-ality. We also investigate [L. Del Debbio, H. Panagopoulos, E. Vicari, hep-th/0407068, to appear in JHEP] the large-N behavior of the topological susceptibility χ in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. The results indicate that χ has a nonvanishing large-N limit for T < Tc, as at T = 0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, χ shows a large suppression. The comparison between the data for N = 4 and N = 6 hints at a vanishing large-N limit for T > Tc.

Phase transition in vector spin glasses

We first give an experimental and theoretical introduction to spin glasses, and then discuss the nature of the phase transition in spin glasses with vector spins. Results of Monte Carlo simulations of the Heisenberg spin glass model in three dimensions are presented. A finite size scaling analysis of the correlation length of the spins and chiralities shows that there is a single, finite-temperature transition at which both spins and chiralities order.

A Peculiar Behavior of the Overlap Distribution in a Heisenberg Spin Glass Model in Three Dimensions

We have studied the phase transition of the ±J Heisenberg model in three dimensions. Using the exchange Monte Cairo method, we have investigated the spin-overlap distribution near the SG transition temperature. By selecting the order parameter as the maximum value of the spin overlap of the diagonal components under the uniform rotations, the calculated overlap distribution suggests the appearance of a peculiar type of replica-symmetry breaking which is similar to the one found in the chirality-overlap distribution by Hukushima and Kawamura. This result may explain absence of any crossing of the Binder parameter of the spin at a finite SG transition temperature.

Orbital and spin interplay in spin-gap formation in pyroxeneATiSi2O6(A=Na,Li)

Interplay between orbital and spin degrees of freedom is theoretically studied for the phase transition to the spin-singlet state with lattice dimerization in pyroxene titanium oxides ATiSi2O6 (A=Na, Li). For the quasi one-dimensional spin-1/2 systems, we derive an effective spin-orbital-lattice coupled model in the strong correlation limit with explicitly taking account of the t_2g orbital degeneracy, and investigate the model by numerical simulation as well as the mean-field analysis. We find a nontrivial feedback effect between orbital and spin degrees of freedom; as temperature decreases, development of antiferromagnetic spin correlations changes the sign of orbital correlations from antiferro to ferro type, and finally the ferro-type orbital correlations induce the dimerization and the spin-singlet formation. As a result of this interplay, the system undergoes a finite-temperature transition to the spin-dimer and orbital-ferro ordered phase concomitant with the Jahn-Teller lattice distortion. The numerical results for the magnetic susceptibility show a deviation from the Curie-Weiss behavior, and well reproduce the experimental data. The results reveal that the Jahn-Teller energy scale is considerably small and the orbital and spin exchange interactions play a decisive role in the pyroxene titanium oxides.

Two-dimensional Heisenberg model with nonlinear interactions: [formula omitted] corrections

We investigate a two-dimensional classical N-vector model with a generic nearest-neighbor interaction W ( σ i ⋅ σ j ) in the large- N limit, focusing on the finite-temperature transition point at which energy–energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as 1 / N 3 / 2 along the magnetic direction and as 1 / N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for N = ∞ .

Finite temperature transition for 2-flavor lattice QCD at finite isospin density

We simulate 2-flavour lattice QCD at finite isospin chemical potential mu_I, for temperatures close to the finite temperature transition from hadronic matter to a quark-gluon plasma. The mu_I dependence of the transition coupling is observed and used to estimate the decrease in the transition temperature with increasing mu_I. These simulations are performed on an 8^3 times 4 lattice at 3 different quark masses. Our estimate of the magnitude of the fluctuations of the phase of the fermion determinant at small quark-number chemical potential mu, suggest that the position of the small mu and small mu_I transitions should be the same for mu_I=2mu, and we argue that the nature of these transitions should be the same. For all mu_I < m_pi the smoothness of these transitions and the values of the Binder cumulant B_4, indicate that these transitions are mere crossovers, and show no sign of the expected critical endpoint. For mu_I > m_pi and a small isospin (I_3) breaking term lambda, we do find evidence of a critical endpoint which would indicate that, for lambda=0, there is a tricritical point on the phase boundary where the pion condensate evaporates, where this phase transition changes from second to first order.

Topological susceptibility of SU(N) gauge theories at finite temperature

We investigate the large-N behavior of the topological susceptibility in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at Tc. For this purpose, we consider the lattice formulation of the SU(N) gauge theories and perform Monte Carlo simulations for N=4,6. The results indicate that the topological susceptibility has a nonvanishing large-N limit for T<Tc, as at T=0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, the topological susceptibility shows a large suppression. The comparison between the data for N=4 and N=6 hints at a vanishing large-N limit for T>Tc.

The finite temperature transition in (2+1)-flavour QCD with staggered HYP action

We study the finite temperature transition in (2+1)-flavour QCD using Nτ = 4 and 6 lattices with HYP staggered action for different values of the quark masses, including the physical one. We determine the transition temperature in the chiral limit, which turns out to be Tc = (188 ± 11) MeV for Nτ = 4 and Tc = (177 ± 7) MeV for Nτ = 6. For the physical quark (pion) mass the transition is likely to be a crossover which happens roughly at the transition temperature of the chiral limit.

Universality, vortices, and confinement: Modified SO(3) lattice gauge theory at nonzero temperature

We investigate the adjoint SU(2) lattice gauge theory in $3+1$ dimensions with the Wilson plaquette action modified by a ${Z}_{2}$ monopole suppression term. For the zero-twist sector we report on indications for the existence of a finite temperature transition decoupled from the unphysical bulk transitions.

Five-loop epsilon expansion forU(n) U(m) models: finite-temperature phase transition in light QCD

We consider the U(n)xU(m) symmetric Phi^4 Lagrangian to describe the finite-temperature phase transition in QCD in the limit of vanishing quark masses with n=m=N_f flavors and unbroken anomaly at T_c. We compute the Renormalization Group functions to five-loop order in Minimal Subtraction scheme. Such higher order functions allow to describe accurately the three-dimensional fixed-point structure in the plane (n,m), and to reconstruct the line n^+(m,d) which limits the region of second-order phase transitions by an expansion in epsilon=4-d. We always find n^+(m,3)>m, thus no three-dimensional stable fixed point exists for $n=m$ and the finite temperature transition in light QCD should be first-order. This result is confirmed by the pseudo-epsilon analysis of massive six-loop three dimensional series.

Structure of the baryonic flux tube in Nf = 2 lattice QCD at finite temperature

We study the flux tube profile in the baryonic system in full QCD at finite temperature on $N_{t}=8$ lattice. We fix the maximally Abelian gauge and measure the monopole and the photon parts of the Abelian action density, the color electric field and the monopole current on both sides of the finite temperature transition. We demonstrate the disappearance of the flux tube in the high temperature phase.

On the phase structure of a modified SO(3) lattice gauge theory

We investigate the disentanglement of the well-known bulk phase transition from a possible finite temperature phase transition in the adjoint representation SU(2) lattice gauge theory modified by a center-blind Z2 monopole suppression term in the action. The phase structure of such a theory is studied with the help of various parameters: twist variables, Polyakov loop and the Pisa disorder parameter. We find an indication for a finite temperature transition decoupling from the bulk phase transition.

Finite-temperature Mott transition in the two-dimensional Hubbard model

Mott transitions are studied in the two-dimensional Hubbard model by a non-perturbative theory of correlator projection that systematically includes spatial correlations into the dynamical mean-field approximation. Introducing a nonzero second-neighbor transfer, a first-order Mott transition appears at finite temperatures and ends at a critical point or curve.

Profiles of a Broken String in Two-Flavor QCD below and above the Finite Temperature Transition

We study the Abelian flux tube profile of mesonic and the baryonic configurations of static quarks below and above the finite-temperature transition in $N_f=2$ full QCD. To reduce effects of ultra-violet fluctuations we measure Abelian distributions of the action density, the color-electric field and the monopole current after fixing to the maximally Abelian gauge. Changing the distance $R$ between quarks for fixed $T/T_c<1$, one can see a clear signal of string breaking for large $R$. The electric field becomes Coulomb-like and the circulating monopole current disappears. We study also the temperature dependence of the flux profile for fixed $R \approx 0.7$ fm. The disappearance of the squeezed flux is observed clearly above $T_c$. Similar behaviors are observed both in the mesonic and the baryonic systems.