Coupled Ladders in a Magnetic Field

TL;DR

This paper studies phase transitions in two-leg ladder magnetic systems under a magnetic field, analyzing correlation functions, critical temperature behavior, and experimental implications for specific compounds.

Contribution

It provides a quantitative analysis of correlation functions and phase transition behavior in coupled ladder systems under magnetic fields, including the critical temperature shape and universality class.

Findings

Critical temperature T_c(h) exhibits a camel-like shape with a local minimum.

T_c scales as (h - h_{c1})^{2/3} near the lower critical field.

The phase transition belongs to the Bose condensation universality class.

Abstract

We investigate the phase transitions in two-leg ladders systems in the incommensurate phase, for which the gap is destroyed by a magnetic field ($h_{c1}< h$) and the ladder is not yet totally saturated ($h < h_{c2}$). We compute quantitatively the correlation functions as a function of the magnetic field for an isolated strong coupling ladder $J_\perp \gg J_\parallel$ and use it to study the phase transition occuring in a three dimensional array of antiferromagnetically coupled ladders. The three dimensional ordering is in the universality class of Bose condensation of hard core bosons. We compute the critical temperature $T_c(h)$ as well as various physical quantities such as the NMR relaxations rate. $T_c$ has an unusual camel-like shape with a local minimum at $h=(h_{c1}+h_{c2})/2$ and behaves as $T_c \sim (h-h_{c1})^{2/3}$ for $h\sim h_{c1}$. We discuss the experimental consequences for compounds such as Cu_2(C_5H_{12}N_2)_2Cl_4