Geodesic
Weak first-order transition and pseudoscaling behavior in the~universality class of the~$O(N)$ Ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 310-323

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Using Monte Carlo and renormalization group methods, we investigate systems with critical behavior described by two order parameters: continuous $($vector$)$ and discrete (scalar). We consider two models of classical three-dimensional Heisenberg magnets with different numbers of spin components $N=1,\dots,4$: the model on a cubic lattice with an additional competing antiferromagnetic exchange interaction in a layer and the model on a body-centered lattice with two competing antiferromagnetic interactions. In both models, we observe a first-order transition for all values of $N$. In the case where competing exchanges are approximately equal, the first order of a transition is close to the second order, and pseudoscaling behavior is observed with critical exponents differing from those of the $O(N)$ model. In the case $N=2$, the critical exponents are consistent with the well-known indices of the class of magnets with a noncollinear spin ordering. We also give a possible explanation of the observed pseudoscaling in the framework of the renormalization group analysis.
Mots-clés : phase transition
Keywords: Monte Carlo method, renormalization group, frustrated magnet, pseudoscaling. 
@article{TMF_2019_200_2_a10,
     author = {A. O. Sorokin},
     title = {Weak first-order transition and pseudoscaling behavior in the~universality class of the~$O(N)$ {Ising} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {310--323},
     publisher = {mathdoc},
     volume = {200},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a10/}
}
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A. O. Sorokin. Weak first-order transition and pseudoscaling behavior in the~universality class of the~$O(N)$ Ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 2, pp. 310-323. http://geodesic.mathdoc.fr/item/TMF_2019_200_2_a10/