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We analyze the properties of a general Ginzburg-Landau free energy withcompeting order parameters, long-range interactions, and global constraints(e.g., a fixed value of a total ``charge'') to address the physics of stripephases in underdoped high-Tc and related materials. For a local free energylimited to quadratic terms of the gradient expansion, only uniform orphase-separated configurations are thermodynamically stable. ``Stripe'' orother non-uniform phases can be stabilized by long-range forces, but can onlyhave non-topological (in-phase) domain walls where the components of theantiferromagnetic order parameter never change sign, and the periods of chargeand spin density waves coincide. The antiphase domain walls observedexperimentally require physics on an intermediate lengthscale, and they areabsent from a model that involves only long-distance physics. Dense stripephases can be stable even in the absence of long-range forces, but domain wallsalways attract at large distances, i.e., there is a ubiquitous tendency tophase separation at small doping. The implications for the phase diagram ofunderdoped cuprates are discussed.Comment: 18 two-column pages, 2 figures, revtex+eps

Topological doping and the stability of stripe phases