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arXiv:2104.11818 · Physical review. E

Unconventional low-temperature features in the one-dimensional frustrated q -state Potts model

Yu. D. Panov, Onofre Rojas

Published Jun 2, 2021• 18 citations
arXivHTMLPDF

Abstract

Here we consider a one-dimensional q-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit strong acute peaks similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where this anomalous feature occurs we call the pseudocritical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudocritical exponents that satisfy a class of universality previously identified in the literature for other one-dimensional models; these pseudocritical exponents are for correlation length ν=1, specific heat α=3, and magnetic susceptibility μ=3.

DOI
10.1103/physreve.103.062107

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Here we consider a one-dimensional q-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits unusual behavior in the low-temperature region, where we observe an anomalous vigorous change in the entropy for a given temperature. There is a steep behavior at a given temperature in entropy as a function of temperature, quite similar to first-order discontinuity, but there is no jump in the entropy. Similarly, second derivative quantities like specific heat and magnetic susceptibility also exhibit strong acute peaks similar to second-order phase transition divergence, but once again there is no singularity at this point. Correlation length also confirms this anomalous behavior at the same given temperature, showing a strong and sharp peak which easily one may confuse with a divergence. The temperature where this anomalous feature occurs we call the pseudocritical temperature. We have analyzed physical quantities, like correlation length, entropy, magnetization, specific heat, magnetic susceptibility, and distant pair correlation functions. Furthermore, we analyze the pseudocritical exponents that satisfy a class of universality previously identified in the literature for other one-dimensional models; these pseudocritical exponents are for correlation length ν=1, specific heat α=3, and magnetic susceptibility μ=3.
The q-state Potts model on a diamond chain has mathematical significance in analyzing phase transitions and critical behaviors in diverse fields, including statistical physics, condensed matter physics, and materials science. By focusing on the three-state Potts model on a diamond chain, we reveal rich and analytically solvable behaviors without phase transitions at finite temperatures. Upon investigating thermodynamic properties such as internal energy, entropy, specific heat, and correlation length, we observe sharp changes near zero temperature. Magnetic properties, including magnetization and magnetic susceptibility, display distinct behaviors that provide insights into spin configurations in different phases. However, the Potts model lacks genuine phase transitions at finite temperatures, in line with the Peierls argument for one-dimensional systems. Nonetheless, in the general case of an arbitrary q state, magnetic properties such as correlation length, magnetization, and magnetic susceptibility exhibit intriguing remnants of a zero-temperature phase transition at finite temperatures. Furthermore, residual entropy uncovers unusual frustrated regions at zero-temperature phase transitions. This feature leads to the peculiar thermodynamic properties of phase boundaries, including a sharp entropy change resembling a first-order discontinuity without an entropy jump, and pronounced peaks in second-order derivatives of free energy, suggestive of a second-order phase transition divergence but without singularities. This unusual behavior is also observed in the correlation length at the pseudocritical temperature, which could potentially be misleading as a divergence.
Quasicritical exponents of one-dimensional models displaying a quasitransition at finite temperatures are examined in detail. The quasitransition is characterized by intense sharp peaks in physical quantities such as specific heat and magnetic susceptibility, which are reminiscent of divergences accompanying a continuous (second-order) phase transition. The question whether these robust finite peaks follow some power law around the quasicritical temperature is addressed. Although there is no actual divergence of these quantities at a quasicritical temperature, a power-law behavior fits precisely both ascending as well as descending parts of the peaks in the vicinity but not too close to a quasicritical temperature. The specific values of the quasicritical exponents are rigorously calculated for a class of one-dimensional models (e.g., Ising-XYZ diamond chain, coupled spin-electron double-tetrahedral chain, Ising-XXZ two-leg ladder, and Ising-XXZ three-leg tube), whereas the same set of quasicritical exponents implies a certain "universality" of quasitransitions of one-dimensional models. Specifically, the values of the quasicritical exponents for one-dimensional models are: α=α^{'}=3 for the specific heat, γ=γ^{'}=3 for the susceptibility and ν=ν^{'}=1 for the correlation length.
Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=12S=\frac{1}{2}S=21​ spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L=200L=200L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multiparticle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.
A few paradigmatic one-dimensional lattice-statistical spin models have recently attracted a vigorous scientific interest owing to their peculiar thermodynamic behavior, which is highly reminiscent of a temperature-driven phase transition. The pseudotransitions of one-dimensional lattice-statistical spin models differ from actual phase transitions in several important aspects: the first-order derivatives of the Gibbs free energy such as entropy or magnetization exhibit near a pseudo-transition an abrupt continuous change instead of a true discontinuity, whereas the second-order derivatives of the Gibbs free energy such as specific heat or susceptibility display near a pseudo-transition a vigorous finite peak instead of an actual power-law divergence. In the present chapter we will comprehensively examine a pseudo-critical behavior of the spin-1/2 Ising diamond and tetrahedral chains by a detailed examination of basic magnetothermodynamic quantities such as the entropy, specific heat and susceptibility. It will be demonstrated that density plots of these magnetothermodynamic quantities provide a useful tool for establishing a finite-temperature diagram, which clearly delimits boundaries between individual quasi-phases in spite of a lack of true spontaneous long-range order at any nonzero temperature. It is suggested that a substantial difference between the degeneracies of two ground states of the spin-1/2 Ising diamond and tetrahedral chains is an essential prerequisite for observation of a relevant pseudo-critical behavior in a close vicinity of their ground-state phase boundary.
We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.
Recently, a kind of finite-temperature pseudotransition was observed in several quasi-one-dimensional models. In this work, we consider a genuine one-dimensional extended Hubbard model in the atomic limit, influenced by an external magnetic field and with the arbitrary number of particles controlled by the chemical potential. The one-dimensional extended Hubbard model in the atomic limit was initially studied in the seventies and has been investigated over the past decades, but it still surprises us today with its fascinating properties. We rigorously analyze its low-temperature behavior using the transfer matrix technique and provide accurate numerical results. Our analysis confirms that there is an anomalous behavior in the half-filled band, specifically occurring between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. Previous investigations did not deeply identify this anomalous behavior, maybe due to the numerical simplicity of the model, but from an analytical point of view this is not so easy to manipulate algebraically because one needs to solve an algebraic cubic equation. In this study, we explore this behavior and clearly distinguish the pseudotransition, which could easily be mistaken with a real phase transition. This anomalous behavior mimics features of both first- and second-order phase transitions. However, due to its nature, we cannot expect a finite-temperature phase transition in this model.