interaction
1998-05
2022-01-01T18:08
97-103
Quantum rotors with regular frustration and the quantum Lifshitz point
Fisher renormalisation
Hamiltonian
zero-temperature quantum phase transition
phase
renormalisation
regular frustration
helical-para phase
renormalisation group flow behaviour
transition
renormalisation technique
articles
diagram
phase transition
spherical limit
ferro-para
spatial dimensions
helical phase
component quantum rotor Hamiltonian
standard momentum space renormalisation technique
https://scigraph.springernature.com/explorer/license/
quantum Lifshitz point
rotor Hamiltonian
dimensions
presence
upper critical dimensionality
corresponding Gaussian model
quantum rotor Hamiltonian
exponent
false
space renormalisation technique
multicritical point
frustration
isotropic Lifshitz points
renormalisation flow equations
model
paramagnetic phase
DU
Lifshitz point
group flow behaviour
quantum fluctuations
momentum space renormalisation technique
equations
fluctuations
unity
classical Lifshitz point
dimensionality
vicinity
https://doi.org/10.1007/s100510050287
limit
flow behavior
point
rotor
1998-05-01
quantum phase transition
quantum rotor
Gaussian model
en
critical dimensionality
cases
quantum paramagnetic phase
Abstract: We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit (\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\setlength{\oddsidemargin}{-69pt}
\begin{document}$$(n \to \infty )$$
\end{document})one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by du = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (\documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$(n \to \infty )$$
\end{document}). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation.
phase diagram
article
relation
behavior
anisotropic Lifshitz point
dynamical exponent
technique
neighborhood
spherical model
flow equations
1286-4862
Springer Nature
1155-4304
The European Physical Journal B
pub.1003648135
dimensions_id
Chakrabarti
B.K.
1
Physical Sciences
Atomic, Molecular, Nuclear, Particle and Plasma Physics
Springer Nature - SN SciGraph project
Saha Institute of Nuclear Physics, 1/AF Bidhannagar, 700064, Calcutta, India
Saha Institute of Nuclear Physics, 1/AF Bidhannagar, 700064, Calcutta, India
Dutta
A.
Indian Association for the Cultivation of Science, Jadavpur, 700032, Calcutta, India
Indian Association for the Cultivation of Science, Jadavpur, 700032, Calcutta, India
J.K.
Bhattacharjee
10.1007/s100510050287
doi
3