Effective theory of the phase transition in Heisenberg stacked triangular antiferromagnets (original) (raw)
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Phase transition in Heisenberg stacked triangular antiferromagnets: End of a controversy
Physical Review E, 2008
By using the Wang-Landau flat-histogram Monte Carlo (MC) method for very large lattice sizes never simulated before, we show that the phase transition in the frustrated Heisenberg stacked triangular antiferromagnet is of first-order, contrary to results of earlier MC simulations using oldfashioned methods. Our result lends support to the conclusion of a nonperturbative renormalization group performed on an effective Hamiltonian. It puts an end to a 20-year long controversial issue. PACS numbers: 75.10.-b General theory and models of magnetic ordering ; 75.40.Mg Numerical simulation studies
Critical behavior of the antiferromagnetic Heisenberg model on a stacked triangular lattice
1994
We estimate, using a large-scale Monte Carlo simulation, the critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice. We obtain the following estimates: γ/ν = 2.011 ± .014, ν = .585 ± .009. These results contradict a perturbative 2 + ǫ Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour. While these results may be coherent with 4 − ǫ results from Landau-Ginzburg analysis, they show the existence of an unexpectedly rich structure of the Renormalization Group flow as a function of the dimensionality and the number of components of the order parameter.
Stacked triangular XY antiferromagnets: End of a controversial issue on the phase transition
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We show in this paper by using the Wang-Landau flat-histogram Monte Carlo method that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative renormalization group, putting an end to a long-standing controversial issue. PACS numbers: 75.10.-b General theory and models of magnetic ordering ; 75.40.Mg Numerical simulation studies
27. ON THE NATURE OF THE PHASE TRANSITION IN HELIMAGNETS
The nature of the phase transition in body-centered tetragonal helimagnets with both XV and Heisenberg spins is studied by extensive Monte Carlo simulati.ons. In the XV case, evidence of a first order transition associated with the loss of helical ordering is found. The dependence on the tur.n angle. Q is shown.
Phys Rev B, 1997
The nonlinear-sigma model and its generalization on N-component spins, the O(N) model, are considered to describe thermodynamics of a quantum quasi-two-dimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Néel temperature, and spin-correlation function are calculated to first order of the 1/N expansion. A description of crossover from a 2D-like to 3D regime of sublattice magnetization temperature dependence is obtained. The values of the critical exponents derived are Beta=0.36, eta=0.09. An account of the corrections to the standard logarithmic term of the spin-wave theory modifies considerably the value of the Néel temperature. The thermodynamic quantities calculated are universal functions of the renormalized interlayer coupling parameter. The renormalization of the interlayer coupling parameter turns out to be considerably temperature dependent. A good agreement with experimental data on La2CuO4 is obtained. The application of the approach used to the case of a ferromagnet is discussed.
Critical behavior of a two-lattice model of antiferromagnetic phase transitions
Physical Review B, 1975
A two-lattice model of antiferromagnetic phase transitions is discussed in detail, using the Gell-Mann-Low formulation of renormalization-group methods and Wilson's c expansion. Results of a previous work where the model was considered at the critical point are extended to deal with the situation in which the system is near but not at the critical temperature. A discussion is given of the behavior of various physical quantities and thermodynamic functions near the critical point, and of the equation of state. The equation of the critical line is also considered, and it is found that to order e there are no corrections to the mean-field predictions of its critical behavior.
Quantum phase transition in square- and triangular-lattice spin-1/2 antiferromagnets
Physical Review B, 1996
We use the coupled-cluster method to study ground-state properties of anisotropic Sϭ 1 2 antiferromagnets on square and triangular lattices, with the inclusion of arbitrarily long-ranged two-spin correlations. We detect the singularities of various quantities associated with the quantum phase transitions and also compute their critical exponents. The two-spin correlation coefficients for the triangular lattice are found to exhibit an interesting oscillatory behavior in their signs, knowledge of which could assist the implementation of quantum Monte Carlo simulations.
First-Order Phase Transition in Easy-Plane Quantum Antiferromagnets
Physical Review Letters, 2006
Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry phase term that projects out the S = 1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.
Critical dynamics of the body-centered-cubic classical Heisenberg antiferromagnet
Physical Review B, 1996
We have used spin dynamics techniques to perform large-scale simulations of the dynamic behavior of the LϫLϫL body-centered-cubic classical Heisenberg antiferromagnet with Lр48 at a range of temperatures above and below as well as at the critical point T c. The temporal evolutions of the spin configurations were determined numerically from coupled equations of motion for individual spins by a fourth-order predictorcorrector method, with initial spin configurations generated by Monte Carlo simulations. The neutron scattering function S(q,) was calculated from the space-and time-displaced spin-spin correlation function. We used a previously developed dynamic finite-size scaling theory to extract the dynamic critical exponent z from S(q,) at T c. Our results are in agreement with the theoretical prediction of zϭ1.5 and with experimental results; however, we find that the asymptotic regime was only entered at LϷ30. In the analysis of the form of the transverse and longitudinal components of S(q,) we found that a central diffusion peak appears below T c predominantly in the longitudinal component and remains present through and above T c. The transverse component of the spin-wave peak is Lorentzian below T c but for TуT c is described best by a more complex functional form. Below T c we see evidence of multiple spin-wave peaks in the longitudinal component. ͓S0163-1829͑96͒02138-8͔
Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
Journal of Statistical Mechanics: Theory and Experiment, 2005
Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, d ≥ 2 but exhibit only quasi long range order, with power law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude λ, as well as an adjustable power-law 1/|x| α , using a combination of quantum Monte Carlo and analytic methods: spin-wave, large-N non-linear σ model, and renormalization group methods. We map out the phase diagram in the λ-α plane and study the nature of the critical line separating the phases with long range and quasi long range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z < 1.