A study of the bulk phase transitions of the SU(2) lattice gauge theory with mixed action

Using the finite size scaling theory, we reexamine the nature of the bulk phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice gauge theory at β_A = 1.25 where previous finite size scaling investigations of the deconfinement phase transition showed it to be of first order for temporal lattices with four sites. Our simulations on N⁴ lattices with N = 6, 8, 10, 12 and 16 show an absence of a first order bulk phase transition. We find the discontinuity in the average plaquette to decrease approximately linearly with N. Correspondingly, the plaquette susceptibility grows a lot slower with the 4-volume of the lattice than expected from a first order bulk phase transition.     

Critical behavior of the heat capacity of the manganite La<Subscript>0.87</Subscript>K<Subscript>0.13</Subscript>MnO<Subscript>3</Subscript>

The heat capacity of the manganite La_0.87K_0.13MnO₃ has been measured in the temperature range 80–350 K. The nature of the ferromagnetic phase transition and the critical properties of heat capacity near the Curie temperature have been studied. The regularities of variations in the universal critical parameters near the phase transition point have been established. The calculated critical exponent and amplitudes of the heat capacity with allowance for corrections on the scaling (α = −0.13 and A ⁺/A ⁻ = 1.178) correspond to the critical behavior of the 3D Heizenberg model.     

Critical parameters near the ferromagnetic-paramagnetic phase transition in La0.7A0.3(Mn1−xbx)O3 (A=Sr; B=Ti and Al; x=0.0 and 0.05) compounds

The critical parameters provide important information concerning the interaction mechanisms near the paramagnetic-to-ferromagnetic transition. In this paper, we present a thorough study for the critical behavior of La_0.7A_0.3(Mn_1−xB_x)O₃ (A=Sr; B=Ti and Al; x=0.0 and 0.05) polycrystalline samples near ferromagnetic-paramagnetic phase transition temperature by analyzing isothermal magnetization data. We have analyzed our dc-magnetization data near the transition temperature with the help of the modified Arrot plot, Kouvel-Fisher method. We have determined the critical temperature T_C and the critical parameters β, γ and δ. With the values of T_C, β and γ, we plot M×(1−T/T_C)^−β vs. H×(1−T/T_C)^−γ. All the data collapse on one of the two curves. This suggests that the data below and above T_C obey scaling, following a single equation of state. Critical parameters for x=0 and x_Ti=0.05 samples are between those predicted for a 3D-Heisenberg model and mean-field theory and for x_Al=0.05 samples the values obtained for the critical parameters are close to those predicted by the mean-field theory.     

Heat capacity of the La<Subscript>0.9</Subscript>Ag<Subscript>0.1</Subscript>MnO<Subscript>3</Subscript> manganite near the curie temperature

The heat capacity of the La_0.9Ag_0.1MnO₃ manganite is measured in the temperature range 77–350 K and studied in detail in the vicinity of the Curie temperature for the first time. The regularities of the variation in the universal critical parameters in the vicinity of the phase transition point are established. The critical exponent and the amplitude of the heat capacity are calculated to be α = ?0.127 and A ⁺/A ^? = 1.146 with due regard for the scaling corrections. These parameters correspond to the critical behavior within the three-dimensional Heisenberg model. The size of ferromagnetic droplets in the paramagnetic range at T > T _C is estimated as ξ ≈ 19 Å. The results obtained are analyzed thoroughly and compared with theoretical data for a number of model systems.     

Multi-grid Monte Carlo via XY embedding. General theory and two-dimensional O(N)-symmetric non-linear σ-models

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an XY model into the target model, and we study its mathematical properties for a variety of non-linear σ-models. We then apply the method to the two-dimensional O(N)-symmetric nonlinear σ-models (also called N-vector models) with N = 3,4,8 and study its dynamic critical behavior. Using lattices up to 256 × 256, we find dynamic critical exponentsZ_int, M² 0.70 ± 0.08, 0.60 ± 0.07, 0.52 ± 0.10 for N = 3, 4, 8, respectively (subjective 68% confidence intervals). Thus, for these asymptotically free models, critical slowing down is greatly reduced compared to local algorithms, but not completely eliminated; and the dynamic critical exponent does apparently vary with N. We also analyze the static data for N = 8 using a finite-size scaling extrapolation method. The correlation length ξ agrees with the four-loop asymptotic-freedom prediction to within 1 % over the interval 12 ⪅ ξ ⪅ 650.     

Quasi-one-dimensional quantum spin liquid in the Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.     

Setting bounds on critical exponents with event-by-event analysis of nuclear fragmentation data

And analysis of recent ISiS data [1] is performed and a comparison with percolation-based theories is conducted. We pay particular attention to detector acceptance corrections as well as the role of sequential decays of excited pre-fragments. The corrected data are subjected to a scaling analysis. We find evidence for a continuous phase transition in these nuclear multi-fragmentation events and extract the value for the critical exponents: σ=0.5±0.1 and τ=2.35±0.05. In addition, we find T _c=8.3±0.2 MeV.     

Correction to scaling critical exponents and amplitudes for amorphous Fe–Mn–Zr alloys

Asymptotic and leading correction to scaling critical exponents and amplitudes have been determined for quenched amorphous Fe_90−yMn_yZr₁₀ (y=0–8) ferromagnets through an elaborate analysis of temperature dependence of spontaneous magnetization, zero-field susceptibility and low-field AC susceptibility data obtained in the asymptotic critical region. From this analysis, it is found that the values of the critical exponents and amplitudes do not depend on the alloy composition and are in good agreement with the values predicted for three-dimensional Heisenberg ferromagnet system. The observed experimental results are consistent with the concept of scaling in that the exponent equalities β=γ(δ−1) and α=2(1−β)−γ are obeyed to a high degree of accuracy. These results show that both amorphous and crystalline materials behave similarly in the critical region though amorphous alloys show a wide asymptotic critical region than the crystalline materials. The presence of disorder does not seem to have any influence on critical behavior of the system investigated in the present work.     

Specific heat and magnetic susceptibility of single-crystalline ZnCr2−xAlxSe4 (x=0.15, 0.23)

A correlation between the second critical field H_c2 of the helix to paramagnetic transition and the magnetic specific heat C-peak was found in ZnCr_2−xAl_xSe₄ spinel single crystals with x=0.15, 0.23. The specific heat peak is anomalously sharp for all finite magnetic fields used here and this points to a first order magneto-structural transition (from cubic to tetragonal symmetry). The C(T)-peak is increasingly suppressed as the external field increases. Approaching the Neel temperature T_N, a broad ac-magnetic susceptibility peak is observed for zero dc-magnetic field. That peak does not show an energy loss and thus points towards a return to a second order type of transition. The magnetic contribution to the specific heat displays a sharp peak at T_N and is maximal at the spin fluctuation temperature T_sf=34 K. T_sf is related to the maximum of the magnetic susceptibility at T_m=40 K (at 50 kOe) in the spin fluctuation region, as evidenced by the entropy exceeding 90% of the entropy calculated classically for the complete alignment of the Cr spins, (2−x)R ln(2S+1). The X-ray photoelectron spectroscopy (XPS) data indicate that Al-substitution does not affect Cr³⁺ 3d³ electronic configuration.     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

Magnetic phases of amorphous transition metal-metalloid alloys

Hysteresis loop and ac susceptibility measurements were performed on three series of amorphous alloys: (A_wB_1-w)₇₅P₁₆B₆Al₃, where (A, B) are (Fe, Ni), (Co, Ni) and (Fe, Mn). Upon cooling, low w alloys undergo paramagne t to spin glass transitions. Alloys with higher w first experience a Curie transition to a ferromagnetic state, and then a spin freezing transition to a spin glass state. the T dependence of the width of the ac hysteresis loop is used to determine the spin freezing transition temperature. A magnetic phase diagram is presented for each alloy series and the value of w required for ferromagnetism, w_C, is determined. When measured in the presence of small constant fields, the ac susceptibility of alloys with w just above w_C has maxima near both transition temperatures. The field and temperature dependences of the peaks are explained by scaling arguments, used to determine the critical exponent δ for the Curie transition, and suggest that a similar scaling law holds for the ferromagnet to spin glass transition.     

A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude η_c at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. η^LC_C<η^F_C. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.     

The Kosterlitz-Thouless universality class

We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of Lee-Yang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY model and the c]osely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatible with those of the XY model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless.     

Electro-excitation amplitudes of the Δ-isobar in the Skyrme model

Electro magnetic transition form factors for the excitation of the Δ33-resonance are evaluated in the Skyrme model. They crucially rely on rotationally induced deformations of the hedgehog soliton which are suppressed by two N _C-orders as compared to the leading parts of the isovector current. Partial photon coupling through vector mesons is included in a schematic way. Recoil corrections are approximated by a boost to the equal-velocity frame. The results for the photodecay amplitudes agree with experimental numbers and the shapes of M1, E2, C2— transition form factors show essential features as observed in electro-excitation experiments.     

Finite size scaling for O(N) φ4-theory at the upper critical dimension

A finite size scaling theory for the partition function zeroes and thermodynamic functions of O(N) φ⁴-theory in four dimensions is derived from renormalization group methods. The leading scaling behaviour is mean-field like with multiplicative logarithmic corrections which are linked to the triviality of the theory. These logarithmic corrections are independent of N for odd thermodynamic quantities and associated zeroes and are N dependent for the even ones. Thus a numerical study of finite size scaling in the Ising model serves as a non-perturbative test of triviality of φ⁴₄-theories for all N.     

Non-eikonal effects in high-energy scattering IV. Inelastic scattering

We calculate amplitudes of inelastically scattered high-energy projectiles. For the example of scattering on ¹²C (T_p = 1 GeV) we demonstrate sizeable non-eikonal corrections in diffraction extrema even for relatively small q². At least part of the anomaly in the 3-distribution may be due to these non-eikonal effects.     

Universality of the ratio of the critical amplitudes of the magnetic susceptibility in a two-dimensional ising model with nonmagnetic impurities

The behavior of the magnetic susceptibility of a two-dimensional Ising model with nonmagnetic impurities is investigated numerically. A new method for determining the critical amplitudes and critical temperature is developed. The results of a numerical investigation of the ratio of the critical amplitudes of the magnetic susceptibility are presented. It is shown that the ratio of the critical amplitudes is universal right up to impurity concentrations q ≤ 0.25 (the percolation point of a square lattice is q _c = 0.407254). The behavior of the effective critical exponent γ(q) of the magnetic susceptibility is discussed. Apparently, a transition from Ising-type universal behavior to percolation behavior should occur in a quite narrow concentration range near the percolation point of the lattice.     

Polymers and g|φ|4 theory in four dimensions

We investigate the approach to the critical point and the scaling limit of a variety of models on a four-dimensional lattice, including g|φ|₄⁴ theory and the self-avoiding random walk. Our results, both theoretical and numerical, provide strong evidence for the triviality of the scaling limit and for logarithmic corrections to mean field scaling laws, as predicted by the perturbative renormalization group. We relate logarithmic corrections to scaling to the triviality of the scaling limit. Our numerical analysis is based on a novel, high-precision Monte Carlo technique.     

ε-expansion calculations for spin-glasses

The critical properties of the spin-glass transition proposed by Edwards and Anderson are studied using the minimal subtraction method. The universal ratio of the second correction to scaling amplitude to the square of the first for the order parameter susceptibility χ₀ is calculated to first order in ε(ε=6?d). Comparison is made with Fisch and Harris' high temperature series analysis which incorporated Rudnick-Nelson-type corrections to scaling. Within the same formalism the critical exponents are calculated to second order in ε. They agree with the first order ε expansion of Harris, Lubensky and Chen.     

Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach

We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity with R²-interaction on spherical topologies, employing Regge's formulation. We attempt to measure the string susceptibility exponent γ_str by using a finite-size scaling Ansatz in the expectation value of R², as has been done in a previous study by Bock and Vink (Nucl. Phys. B 438 (1995) 320). By considerably extending the range and statistics of their study we find that this Ansatz is plagued by large systematic errors. The R² specific string susceptibility exponent γ_str^′ is found to agree with theoretical predictions, but its determination also is subject to large systematic errors and the presence of finite-size scaling corrections. To circumvent this obstacle we suggest a new scaling Ansatz which in principle should be able to predict both, γ_str and γ_str^′. First results indicate that this requires large system sizes to reduce the uncertainties in the finite-size scaling Ansätze. Nevertheless, our investigation shows that within the achievable accuracy the numerical estimates are still compatible with analytic predictions, contrary to the recent claim by Bock and Vink.