Ordered vs Disordered: Correlation Lengths of 2D Potts Models at \beta_t

We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $\beta_t$ in the disordered and ordered phase. Our results for the correlation length $\xi_d(\beta_t)$ in the disordered phase are compatible with an analytic formula. Estimates of the correlation length $\xi_o(\beta_t)$ in the ordered phase yield strong numerical evidence that $R \equiv \xi_o(\beta_t)/\xi_d(\beta_t) = 1$.Comment: 3 pages, uuencoded compressed postscript file, contribution to the LATTICE'94 conferenc

Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg Model

We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.Comment: 9 pages, FUB-HEP 9/92, HLRZ Preprint 56/92, August 199

Condensation of vortices and disorder parameter in 3d Heisenberg model

The 3d Heisenberg model is studied from a dual point of view. It is shown that the disordered phase corresponds to condensation of vortices in the vacuum, and the critical indices are computed from the corresponding disorder parameter.Comment: LATTICE98(spin

Comment on "Critical properties of highly frustrated pyrochlore antiferromagnets"

We argue that the analysis of Reimers {\it et al.} [ Phys. Rev. B {\bf 45}, 7295 (1992)] of their Monte Carlo data on the Heisenberg pyrochlore antiferromagnet, which suggests a new universality class, is not conclusive. By re-analysis of their data, we demonstrate asymptotic volume dependence in some thermodynamic quantities, which suggests the possibility that the transition may be first order.Comment: 5 pages (RevTex 3.0), 3 figures available upon request, CRPS-93-0

High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model

We report measurements of the critical exponents of the classical three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with $L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long single-cluster Monte Carlo simulations near the phase transition. We compute high precision estimates of the critical coupling $K_c$, Binder's parameter $U^* and the critical exponents$\nu,\beta / \nu, \eta$, and$\alpha / \nu$, using extensively histogram reweighting and optimization techniques that allow us to keep control over the statistical errors. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition as compared to local update algorithms. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first version arrived incomplete due to mailer problems

Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular Ising Antiferromagnet

Histogram Monte-Carlo simulation results are presented for the magnetic-field -- temperature phase diagram of the Ising model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions. Finite-size scaling results for this frustrated system at three points along the paramagnetic transition boundary are presented which strongly suggest a line of triciritcal points at low field and a first-order transition line at higher fields. These results are compared with the corresponding phase diagrams from conventional mean-field theory as well as from the Monte Carlo mean-field calculations of Netz and Berker [Phys. Rev. Lett. {\bf 66}, 377 (1991)].Comment: 6 pages (RevTex 3.0), 8 figures available upon reques

Critical exponents of a three dimensional O(4) spin model

By Monte Carlo simulation we study the critical exponents governing the transition of the three-dimensional classical O(4) Heisenberg model, which is considered to be in the same universality class as the finite-temperature QCD with massless two flavors. We use the single cluster algorithm and the histogram reweighting technique to obtain observables at the critical temperature. After estimating an accurate value of the inverse critical temperature \Kc=0.9360(1), we make non-perturbative estimates for various critical exponents by finite-size scaling analysis. They are in excellent agreement with those obtained with the $4-\epsilon$ expansion method with errors reduced to about halves of them.Comment: 25 pages with 8 PS figures, LaTeX, UTHEP-28

Magnetic Phase Diagram of the Ferromagnetically Stacked Triangular XY Antiferromagnet: A Finite-Size Scaling Study

Histogram Monte-Carlo simulation results are presented for the magnetic-field -- temperature phase diagram of the XY model on a stacked triangular lattice with antiferromagnetic intraplane and ferromagnetic interplane interactions. Finite-size scaling results at the various transition boundaries are consistent with expectations based on symmetry arguments. Although a molecular-field treatment of the Hamiltonian fails to reproduce the correct structure for the phase diagram, it is demonstrated that a phenomenological Landau-type free-energy model contains all the esstential features. These results serve to complement and extend our earlier work [Phys. Rev. B {\bf 48}, 3840 (1993)].Comment: 5 pages (RevTex 3.0), 6 figures available upon request, CRPS 93-

INCONEL 718 SINGLE AND MULTIPASS MODELLING OF HOT FORGING

10International audienceA better understanding of the competition between several mechanisms (dynamic recovery, dynamic recrystallization and plasticity hardening) is crucial for aircraft engine manufacturers. The aim of this paper is to improve the microstructure and therefore the mechanical properties of a nickel based superalloy used for rotating forged pieces. A nickel superalloy microstructure is the result of several successive hot forging processes: multipass processes, with intermediate dwell time and quenching. In this paper, an original three dimensional approach able to simulate these processes is proposed. The specific role of the different steps of the processes is analysed. In this approach, several forging thermo-mechanical parameters are taken into account: the working temperature, the strain rate, the final strain, the interpass time, etc. At high forging temperature, the studied INCONEL 718 presents an austenitic matrix γ (face centred cubic) assumed to be in a single phase. This approach proposes a sequential coupling of two models, one devoted to deformation and the other to recrystallization. Such a coupling enables the estimation of the effect of deformation and of different recrystallization types on mechanical behaviour and on micro-structural evolution. The approach is performed at the grain scale and takes into account the whole thermo-mechanical cycle with a focus on the dynamic behaviour. The first polycrystalline model is based on the plasticity mechanisms at the grains scale. The framework corresponds to finite transformations (large lattice rotations and small elastic strains). The model is implemented in ABAQUS and CAST3M finite element codes. The second model is based on the recrystallization theory and uses a 3D cellular automaton. It describes dynamic recrystallization phenomena such as nucleation-growth and static or post-dynamic recrystallization. Such recrystallization mechanisms were observed during interpass time or during the successive heatings depending on the thermo-mechanical paths used in multipass forging. Dislocation densities are the internal variables common to the two models. The simulations are performed on a 3D Representative Elementary Volume (aggregate) obtained from Electron Back Scattering mapping. Numerical results are compared to experimental microstructures