First and second order transition in frustrated XY systems

Loison, D.; Schotte, K. D.

doi:10.1007/s100510050497

Cited by 95 publications

(114 citation statements)

References 56 publications

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“…Based on Monte Carlo data [3] and on a nonlinear sigma model [4], a tricritical scenario was favored. Others suggest a weakly first-order transition which becomes apparent only very close to the critical temperature T N , whereas further away from T N the data may be described by effective exponents [5][6][7]. An experimental indication for the latter scenario was found recently [8].…”

Section: (Received 30 May 2000)mentioning

confidence: 92%

Chiral Critical Exponents of the Triangular-Lattice AntiferromagnetCsMnBr3as Determined by Polarized Neutron Scattering

et al. 2000

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The critical exponents g c 0.84͑7͒ of the chiral susceptibility above the Néel temperature, T N , and b c 0.44͑2͒ of the average chirality below T N have been determined for the triangular-lattice antiferromagnet CsMnBr 3 by means of polarized neutron scattering. These first experimental values of chiral critical exponents are in line with theoretical predictions and fulfill their scaling relation. The temperature at which the average chirality appears coincides with the spin-order transition temperature, T N .

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Section: (Received 30 May 2000)mentioning

confidence: 92%

Chiral Critical Exponents of the Triangular-Lattice AntiferromagnetCsMnBr3as Determined by Polarized Neutron Scattering

et al. 2000

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“…[11] the results for the XY STA are interpreted as an evidence for mean-field tricritical behavior. Moreover, MC investigations [15] of special lattice spin systems, that on the basis of their symmetry should belong to the chiral universality class, show clearly a first-order transition.…”

mentioning

confidence: 99%

“…This may explain some experiments (for example those for the CsCuCl 3 compound, see, e.g., Refs. [5,6]) and MC studies for special lattice systems [15], where first-order transitions are observed. Beside the conventional critical exponents β, γ, ν, etc... related to the standard spin order, one may consider additional critical exponents related to the behavior of the chiral degrees of freedom.…”

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confidence: 99%

Chiral exponents in frustrated spin models with noncollinear order

2001

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We compute the chiral critical exponents for the chiral transition in frustrated two-and threecomponent spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA). For this purpose, we calculate and analyze the six-loop field-theoretical expansion of the renormalization-group function associated with the chiral operator. The results are in satisfactory agreement with those obtained in the recent experiment on the XY STA CsMnBr3 reported by V. P. Plakhty et al., Phys. Rev. Lett. 85, 3942 (2000), providing further support for the continuous nature of the chiral transition.PACS Numbers: 05.10. Cc, 05.70.Fh, 75.10.Hk, 64.60.Fr, The critical behavior of frustrated spin systems with noncollinear order is still a controversial issue, fieldtheoretical (FT) methods, Monte Carlo (MC) simulations, and experiments providing contradictory results in many cases. At present there is no agreement on the nature of the phase transition, and in particular on the existence of a new chiral universality class [1]. See, e.g., the recent works [2][3][4] and Refs. [5][6][7] for reviews.In magnets noncollinear order is due to frustration that may arise either because of the special geometry of the lattice, or from the competition of different kinds of interactions. Typical examples of systems of the first type are two-and three-component antiferromagnets on stacked triangular lattices [8]. Their behavior at the chiral transition may be modeled by a short-ranged Hamiltonian for N -component spin variables S a , defined on a stacked triangular lattice aswhere J < 0, the first sum is over nearest-neighbor pairs within triangular layers, and the second one is over orthogonal interlayer nearest neighbors. Frustration due to the competition of interactions is realized in helimagnets.In these models frustration is partially released by mutual spin canting and the degeneracy of the ground state is limited to global O(N ) spin rotations and reflections. At criticality one expects a breakdown of the symmetry from O(N ) in the high-temperature phase to O(N − 2) in the low-temperature phase, implying a matrix-like order parameter. In particular, the ground state of the XY systems shows the 120 o structure of Fig. 1, and it is Z 2 chirally degenerate according to whether the noncollinear spin configuration is right-or left-handed. The chiral degrees of freedom are related to the local quantity [1]where the summation runs over the three bonds of the given triangle. The definition of C ab can be straightforwardly generalized to the case of N -component spins. In a recent Letter [3] the issue has been studied by a continuous renormalization-group (RG) approach (see also Refs. [16,17]). The results favor a first-order transition, since no evidence of stable fixed points is found. According to this first-order transition picture, the apparent continuous critical phenomena observed in experiments are interpreted as first-order transitions, weak enough to effectively appear as second-order ones. Note however that the practical i...

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“…It is apparent from Fig.1 that the V L (T, p) value tends to 2/3 at L→∞. Such a behavior is, as has been mentioned above, typical for a second order transition [7]. Phase transition temperature T l (p) determined for all considered systems by the We calculate the static CE for the heat capacity , susceptibility , and order parameter β by means of the finite-size scaling theory (FSST).…”

Section: Results Of Simulationmentioning

confidence: 76%

“…This technique works well at detection of a transition order. One knows the distinctive features inherent in PT [7]: at a first order transition the averaged value V L (T, p) tends to some non-trivial value * V according to the equation…”

Section: Simulation Methodsmentioning

confidence: 99%

Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE

2018

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Abstract. By introducing a small amount of non-magnetic impurities into an antiferromagnetic (AF) two-dimensional (2D) Potts model on a triangular lattice it is that the impurities in spin systems described by this model result in the change of a first order to a second-order phase transition. The systems with linear sizes L × L = N, L = 9-144 are considered. Investigations are performed using the standard Metropolis algorithm along with Monte-Carlo single-cluster Wolff algorithm. On the basis of the theory of finite-size scaling, critical exponents (CE) are calculated: the heat capacity α, the susceptibility γ, the order parameter β, and the CE of the correlation radius υ.

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First and second order transition in frustrated XY systems

Cited by 95 publications

References 56 publications

Chiral Critical Exponents of the Triangular-Lattice AntiferromagnetCsMnBr3as Determined by Polarized Neutron Scattering

Chiral Critical Exponents of the Triangular-Lattice AntiferromagnetCsMnBr3as Determined by Polarized Neutron Scattering

Chiral exponents in frustrated spin models with noncollinear order

Critical properties of 2d disordered 3-state antiferromagnetic potts model ON TRIANGULAR LATTICE

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