Finite size effects around pseudo-transition in one-dimensional models with nearest neighbor interaction

Abstract

Recently gigantic peaks in thermodynamic response functions have been observed at finite temperature for one-dimensional models with short-range coupling, closely resembling a second-order phase transition. Thus, we will analyze the finite temperature pseudo-transition property observed in some one-dimensional models and its relationship with finite size effect. In particular, we consider two chain models to study the finite size effects; these are the Ising-Heisenberg tetrahedral chain and an Ising-Heisenberg-type ladder model. Although the anomalous peaks of these one-dimensional models have already been studied in the thermodynamic limit, here we will discuss the finite size effects of the chain and why the peaks do not diverge in the thermodynamic limit. So, we discuss the dependence of the finite size effects, for moderately and sufficiently large systems, in which the specific heat and magnetic susceptibility exhibit peculiar rounded towering peaks for a given temperature. This behavior is quite similar to a continuous phase transition, but there is no singularity. For moderately large systems, the peaks narrow and increase in height as the number of unit cells is increased, and the location of peak shifts slightly. Hence, one can naively induce that the sharp peak should lead to a divergence in the thermodynamic limit. However, for a rather large system, the height of a peak goes asymptotically to a finite value. Our result confirms the dependence of the peak height with the number of unit cells at the pseudo-critical temperature. We also provide an alternative empirical function that satisfactorily fits specific heat and magnetic susceptibility at pseudo-critical temperature. Certainly, our result is crucial to understand the finite size correction behavior in quantum spin models, which in general are only numerically tractable within the framework of the finite size analysis.

arXiv comment14 pages, 6 figures

References in corpus (20)

• The susceptibility and excitation spectrum of (VO)${}_2$P${}_2$O${}_7$ in ladder and dimer chain models
• Integrable models and quantum spin ladders: comparison between theory and experiment for the strong coupling ladder compounds
• Ground States of Spin-1/2 Triangular Antiferromagnets in a Magnetic Field
• Vigorous thermal excitations in a double-tetrahedral chain of localized Ising spins and mobile electrons mimic a temperature-driven first-order phase transition
• Exactly solvable Ising--Heisenberg chain with triangular XXZ-Heisenberg plaquettes
• Spin frustration of a spin-1/2 Ising-Heisenberg three-leg tube as an indispensable ground for thermal entanglement
• Quasi-phases and pseudo-transitions in one-dimensional models with nearest neighbor interactions
• Thermal entanglement and sharp specific-heat peak in an exactly solved spin-1/2 Ising-Heisenberg ladder with alternating Ising and Heisenberg inter-leg couplings
• Universality and quasicritical exponents of one-dimensional models displaying a quasitransition at finite temperatures
• Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds
• Residual entropy and spin gap in a one-dimensional analog of the pyrochlore antiferromagnet
• Correlation functions for a spin-$\frac{1}{2}$ Ising-XYZ diamond chain: Further evidence for quasi-phases and pseudo-transitions
• Low-temperature thermodynamics of the two-leg ladder Ising model with trimer rungs: A mystery explained
• Phase diagram of a coupled tetrahedral Heisenberg model
• Anomalous thermodynamic response in the vicinity of pseudo-transition of a spin-1/2 Ising diamond chain
• Spin ice in a field: quasi-phases and pseudo-transitions
• Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
• The antiferromagnetic Ising model on the swedenborgite lattice
• Magnetization plateau as a result of the uniform and gradual electron doping in a coupled spin-electron double-tetrahedral chain
• Raman study of spin excitations in the tunable quantum spin ladder Cu(Qnx)(Cl${}_{1-x}$Br${}_x$)${}_2$

Cited by in corpus (3)

• Low temperature pseudo-phase transition in an extended Hubbard diamond chain
• Pseudo-transition between antiferromagnetic and charge orders in a minimal spin-pseudospin model of one-dimensional cuprates
• Spectral mechanism and nearly reducible transfer matrices for pseudotransitions in one-dimensional systems