As established by diffraction techniques Au(110)-͑1 3 2͒, which is missing-row reconstructed at 300 K, consecutively undergoes two phase transitions upon heating: an Ising transition at ഠ 650 K and a 3D roughening transition at ഠ700 K. Our teal space investigation with atomic scale resolution by temperature-variable scanning tunneling microscopy reveals that -contrary to present theoretical models -the Ising transition is due to antiphase domains developing during the 2D roughening of ͑1 3 3͒ steps. The missing-row configuration of interior terrace regions remains completely stable until the 3D roughening temperature, thus ruling out an order-disorder transition via lattice gas formation.[S0031-9007(96)01915-1] PACS numbers: 61.50. Ks, 61.16.Ch, 68.35.Bs, 82.65.Dp Owing to the superior experimental and theoretical standards of surface sciences and thin film technology it nowadays has become feasible to prepare high quality 2D (two-dimensional) systems with long-range periodic order over distances of several hundred nanometers. From a theoretical point of view it is known at least since the celebrated solution of the 2D Ising model by Onsager [1] that 2D systems-as their counterparts 3Dcan undergo phase transitions [2]. Until now several other 2D models have been solved exactly with the methods of statistical mechanics, but the number of experimental realizations of such model systems still is minute. Recently fcc(110) surfaces [ Fig. 1(a)], aside from their importance for catalysis, have attracted considerable interest for the study of phase transitions in 2D. Though discussed controversially for many years, it is now well established that fcc(110) surfaces of transition metals exhibit a pronounced tendency to reconstructions of the MR (missing-row) type either in the clean state or driven by adsorbates [3]. More recently another characteristic feature of fcc(110) surfaces has been discovered, namely, that they undergo a 3D roughening transition at temperatures well below the bulk melting point (see reviews of Refs. [4,5]), which for the unreconstructed surfaces is of the Kosterlitz-Thouless type [6]. In the case of Au (110) and Pt(110), which are ͑1 3 2͒ MR reconstructed already in the ground state [ Fig. 1(b)], the situation is even more complex, as on these two surfaces the processes of deconstruction and roughening are coupled [7]. Whereas on Pt(110) both processes proceed at the same temperature [8], for Au(110) an additional phase transition has been identified from the disappearance of the half-order diffraction spots [9][10][11][12][13]. The respective transition temperature T C given in literature varies between 650 and 735 K, but in any case lies about 50 K below the roughening temperature T R . The critical exponents at T C are in accordance with the 2D Ising universality class [1]. Up to now, however, there is still controversy about the structural models, particularly for the Ising transition [4]. On the basis of Monte Carlo simulations Campuzano et al. [14] suggested a 2D order-disorder transitio...