Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Phase Transition in the n>2 Honeycomb O(n) Model

Wenan Guo, Henk W. J. Blöte, Fa Yueh Wu

Published Oct 30, 2000• 25 citations
Publisher

Abstract

We determine the phase diagram of the O(n) loop model on the honeycomb lattice, in particular, in the range n>2, by means of a transfer-matrix method. We find that, contrary to the prevailing expectation, there is a line of critical points in the range between n = 2 and infinity. This phase transition, which belongs to the three-state Potts universality class, is unphysical in terms of the O(n) spin model, but falls inside the physical region of the n-component corner-cubic model. It can also be interpreted in terms of the ordering of a system of soft particles with hexagonal symmetry.

DOI
10.1103/physrevlett.85.3874

Related papers

Phase Transitions of a Dilute O(n) Model

Wenan Guo, Henk W. J. Blöte, Yuanyuan Liu

We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix. Our results reveal the existence of a tricritical line, parametrized by n , which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point, the tricritical line extends to the n = 2 point describing a tricritical O(2) model.

Communications in Theoretical Physics•Jun 15, 2004•4 citations

PHASE TRANSITIONS IN THE TWO-DIMENSIONAL O(3) MODEL

Henk W. J. Blöte, Wenan Guo

We use Monte Carlo, transfer-matrix and finite-size scaling methods to investigate two-dimensional O (n) models with n > 2, in particular the case n = 3 which includes the classical Heisenberg model. Depending on the type of interaction and the lattice structure, two different types of phase transitions are present. One type resembles the hard-hexagon transition and occurs in the loop representation of the honeycomb O (n) model. The other type is a first-order transition which occurs for spin-spin interactions that are strongly nonlinear in the neighbor-spin products. When the nonlinearity is decreased, the first-order line ends in a critical point. The existence of the first-order line is in agreement with mean-field theory as well as with high- and low-temperature approximations.

International Journal of Modern Physics B•Jun 20, 2002•3 citations

Ising-like transitions in the O(n) loop model on the square lattice

Zhe Fu, Wenan Guo, Henk W. J. Blöte

We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points.

arXiv:1301.6828•Physical Review E•May 14, 2013•9 citations

FIRST AND SECOND ORDER TRANSITIONS IN DILUTE O (n) MODELS

Wenan Guo, Henk W. J. Blöte, Bernard Nienhuis

We explore the phase diagram of an O (n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O (n) model, so that n is not restricted to positive integers. For low activities of the vacancies, we observe critical points of the known universality class. At high activities the transition becomes first order. For n=0 the model includes an exactly known theta point, used to describe a collapsing polymer in two dimensions. When we vary n from 0 to 1, we observe a tricritical point which interpolates between the universality classes of the theta point and the Ising tricritical point.

arXiv:cond-mat/9812270•International Journal of Modern Physics C•Feb 1, 1999•5 citations

Quantum phase transition, O(3) universality class, and phase diagram of the spin- 12 Heisenberg antiferromagnet on a distorted honeycomb lattice: A tensor renormalization-group study

Wei Li, Shou-Shu Gong, Yang Zhao +1 more

The spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the $O(3)$ universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.

arXiv:1005.0932•Physical Review B•May 21, 2010•34 citations

Phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction

Alessandro Campa, Vahan Hovhannisyan, Stefano Ruffo +1 more

Abstract We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-1 Blume–Emery–Griffiths model and solving it by using a Hubbard–Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling K and the temperature T . We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase transition lines. We also prove that, when the nearest-neighbour coupling K is large and negative, the first-order transition temperature becomes asymptotically independent of K .

arXiv:2512.02930•Journal of Statistical Mechanics Theory and Experiment•Feb 1, 2026•0 citations
We determine the phase diagram of the O(n) loop model on the honeycomb lattice, in particular, in the range n>2, by means of a transfer-matrix method. We find that, contrary to the prevailing expectation, there is a line of critical points in the range between n = 2 and infinity. This phase transition, which belongs to the three-state Potts universality class, is unphysical in terms of the O(n) spin model, but falls inside the physical region of the n-component corner-cubic model. It can also be interpreted in terms of the ordering of a system of soft particles with hexagonal symmetry.
We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix and finite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb lattice with vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degrees of freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of a continuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix. Our results reveal the existence of a tricritical line, parametrized by n , which connects the known universality classes of the tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point, the tricritical line extends to the n = 2 point describing a tricritical O(2) model.
We use Monte Carlo, transfer-matrix and finite-size scaling methods to investigate two-dimensional O (n) models with n > 2, in particular the case n = 3 which includes the classical Heisenberg model. Depending on the type of interaction and the lattice structure, two different types of phase transitions are present. One type resembles the hard-hexagon transition and occurs in the loop representation of the honeycomb O (n) model. The other type is a first-order transition which occurs for spin-spin interactions that are strongly nonlinear in the neighbor-spin products. When the nonlinearity is decreased, the first-order line ends in a critical point. The existence of the first-order line is in agreement with mean-field theory as well as with high- and low-temperature approximations.
We explore the phase diagram of the O(n) loop model on the square lattice in the (x,n) plane, where x is the weight of a lattice edge covered by a loop. These results are based on transfer-matrix calculations and finite-size scaling. We express the correlation length associated with the staggered loop density in the transfer-matrix eigenvalues. The finite-size data for this correlation length, combined with the scaling formula, reveal the location of critical lines in the diagram. For n>>2 we find Ising-like phase transitions associated with the onset of a checkerboardlike ordering of the elementary loops, i.e., the smallest possible loops, with the size of an elementary face, which cover precisely one-half of the faces of the square lattice at the maximum loop density. In this respect, the ordered state resembles that of the hard-square lattice gas with nearest-neighbor exclusion, and the finiteness of n represents a softening of its particle-particle potentials. We also determine critical points in the range -2≤n≤2. It is found that the topology of the phase diagram depends on the set of allowed vertices of the loop model. Depending on the choice of this set, the n>2 transition may continue into the dense phase of the n≤2 loop model, or continue as a line of n≤2 O(n) multicritical points.
We explore the phase diagram of an O (n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O (n) model, so that n is not restricted to positive integers. For low activities of the vacancies, we observe critical points of the known universality class. At high activities the transition becomes first order. For n=0 the model includes an exactly known theta point, used to describe a collapsing polymer in two dimensions. When we vary n from 0 to 1, we observe a tricritical point which interpolates between the universality classes of the theta point and the Ising tricritical point.
The spin-12\frac{1}{2}21​ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the O(3)O(3)O(3) universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.
Abstract We derive the phase diagram of the one-dimensional three-state Potts model with an additional mean-field interaction in the canonical ensemble. The free energy is obtained by mapping the model onto the spin-1 Blume–Emery–Griffiths model and solving it by using a Hubbard–Stratonovich transformation combined with the transfer matrix method. A complex structure with lines of first-order transitions, two triple points and a critical point appears at finite temperature. The phase diagram is two-dimensional, since there are two adjustable parameters, the nearest-neighbour coupling K and the temperature T . We show that the phase diagram does not present second-order phase transition lines, due to the fact that the order parameter is not a symmetry-breaking one. Quite remarkably, we are able to determine analytically one of the first-order phase transition lines. We also prove that, when the nearest-neighbour coupling K is large and negative, the first-order transition temperature becomes asymptotically independent of K .