In recent years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order - a new form of matter called a soft quasicrystal [1-4]. Their stability is explained by linking between the microscopic description of the system and its coarse-grained free energy. We show, both theoretically and numerically, that the underlying source of the stability is the existence of two natural length-scales and effective three-body interactions, that emerge from the interplay between energy and entropy. We formulate a coarse-grained free-energy functional for a soft-matter system, composed of isotropic particles, which depends on thermodynamical quantities such as temperature, mean density and the critical temperature for the formation of ordered structures from the uniform liquid phase. Using several pair potentials, we study the formation of periodic and quasiperiodic structures displaying various symmetries, and show how one could design the pair potentials to obtain the required structure.

[1] Zeng et al., Nature 428 (2004) 157.

[2] Hayashida et al., Phys. Rev. Lett. 98 (2007) 195502.

[3] Percec et al., J. Am. Chem. Soc. 131 (2009) 7662.

[4] Talapin et al., Nature 461 (2009) 964.