scholarly journals Example of a first-order Néel to valence-bond-solid transition in two dimensions

2010 ◽  
Vol 82 (17) ◽  
Author(s):  
Arnab Sen ◽  
Anders W. Sandvik
Keyword(s):  
Valence Bond ◽  
Two Dimensions ◽  
First Order ◽  
Valence Bond Solid

scholarly journals First-order Néel to columnar valence bond solid transition in a model square-lattice S=1 antiferromagnet

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Julia Wildeboer ◽  
Nisheeta Desai ◽  
Jonathan D'Emidio ◽  
Ribhu K. Kaul
Keyword(s):  
Valence Bond ◽  
Square Lattice ◽  
First Order ◽  
Valence Bond Solid

From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition

2009 ◽  
Author(s):  
M. Nyfeler ◽  
F.-J. Jiang ◽  
U.-J. Wiese ◽  
S. Chandrasekharan ◽  
Adolfo Avella ◽  
...  
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Valence Bond ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
Valence Bond Solid

A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces

2017 ◽  
Vol 17 (4) ◽  
pp. 601-616 ◽  
Author(s):  
Zheng Li ◽  
Shuo Zhang
Keyword(s):  
Biharmonic Equation ◽  
Two Dimensions ◽  
Zero Order ◽  
Helmholtz Decomposition ◽  
Numerical Verification ◽  
Order Function ◽  
First Order ◽  
Mixed Element ◽  
New Formulation ◽  
Element Method

AbstractThis paper studies the mixed element method for the boundary value problem of the biharmonic equation {\Delta^{2}u=f} in two dimensions. We start from a {u\sim\nabla u\sim\nabla^{2}u\sim\operatorname{div}\nabla^{2}u} formulation that is discussed in [4] and construct its stability on {H^{1}_{0}(\Omega)\times\tilde{H}^{1}_{0}(\Omega)\times\bar{L}_{\mathrm{sym}}^% {2}(\Omega)\times H^{-1}(\operatorname{div},\Omega)}. Then we utilise the Helmholtz decomposition of {H^{-1}(\operatorname{div},\Omega)} and construct a new formulation stable on first-order and zero-order Sobolev spaces. Finite element discretisations are then given with respect to the new formulation, and both theoretical analysis and numerical verification are given.

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