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We revisit the phase transition from the N\'eel ordered to a valence bondsolid (VBS) state in the two-dimensional $J_1-J_2$ antiferromagnetic Heisenbergmodel. In the first part we address the question whether or not this transitioncould be an example of a second order phase transition due to a deconfinementof spinons. We give arguments based on series expansion and spin-wave theorythat this is not the case and the transition is most likely first order. Themethod proposed here to detect first order phase transitions seems to be verysensitive and might be useful in other models as well. In the second part weanalyze possible VBS patterns in the magnetically disordered phase based onnumerical data for different susceptibilities, obtained in the ordered phase,which test the breaking of lattice symmetries. We conclude that a columnardimerization pattern is the most likely candidate.Comment: 7 pages, 7 figures, small changes, references adde

physical review. b, condensed matter and materials physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>J</mml:mi><mml:mn>1</mml:mn><mml:mtext>−</mml:mtext><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:math>model: First-order phase transition versus deconfinement of spinons

J1−J2model: First-order phase transition versus deconfinement of spinons