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Antiferromagnetic Hamiltonians with short-range, non-frustrating interactionsare well-known to exhibit long range magnetic order in dimensions, $d\geq 2$but exhibit only quasi long range order, with power law decay of correlations,in d=1 (for half-integer spin). On the other hand, non-frustrating long rangeinteractions can induce long range order in d=1. We study Hamiltonians in whichthe long range interactions have an adjustable amplitude lambda, as well as anadjustable power-law $1/|x|^\alpha$, using a combination of quantum Monte Carloand analytic methods: spin-wave, large-N non-linear sigma model, andrenormalization group methods. We map out the phase diagram in the lambda-alphaplane and study the nature of the critical line separating the phases with longrange and quasi long range order. We find that this corresponds to a novel lineof critical points with continuously varying critical exponents and a dynamicalexponent, z<1.Comment: 27 pages, 12 figures. RG flow added. Final version to appear in JSTA

Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains