Phase transitions in spin glasses

Whereas there has been a general consensus for some time that Ising spin glasses have a transition at finite temperature in zero field in three dimensions, there has not been general agreement on two other questions concerning phase transitions in spin glasses in three dimensions: (i) is there a transition at finite temperature in isotropic vector spin glasses (such as Heisenberg), and (ii) is there a phase transition (AT line) in a magnetic field in Ising spin glasses? By using Monte Carlo simulations, analyzed with finite-size scaling, I will argue that the answer to the first question is yes, and to the second question is no. (c) 2006 Elsevier B.V. All rights reserved.