article published yes Michael Wassermair author 23d132c4-4e98-11ef-b275-9e8d4cd8c9170009-0003-6339-4051 Gerhard Kahl author Roland Roth author Andrew J. Archer author AnSa department GradSch department Colloidal fluids can exhibit complex phase behavior and determining phase diagrams via experiments or computer simulations can be laborious. We demonstrate that the dispersion relation ω(k), obtained from dynamical density functional theory for the uniform density system, is a highly versatile tool for predicting where in the phase diagram complex crystals form. The sign of ω(k) determines whether density modes with wave number k grow or decay over time. We demonstrate the predictive power by investigating the complex phase behavior of particles interacting via core-shoulder pair potentials. With complementary Monte Carlo simulations, we show that regions of the phase diagram where ωðkÞ has one or several unstable (growing) wave numbers are also where crystalline phases occur. Going further, by tuning these unstable wave numbers via the interaction-potential and state-point parameters, we design systems with quasicrystals in the phase diagram. We identify a system with a certain shoulder range exhibiting at least ten different phases. Our general approach accelerates considerably the mapping of complex phase diagrams, crucial for the design of new materials. https://research-explorer.ista.ac.at/download/21764/21769/2026_PhysicalReviewLetters_Wassermair.pdf application/pdfno American Physical Society2026 eng 0031-9007 1079-7114 2603.1891810.1103/nbvt-fgjy 13614 M. Wassermair, G. Kahl, R. Roth, and A. J. Archer, “Navigating complex phase diagrams in soft matter systems,” <i>Physical Review Letters</i>, vol. 136, no. 14. American Physical Society, 2026. Wassermair M, Kahl G, Roth R, Archer AJ. 2026. Navigating complex phase diagrams in soft matter systems. Physical Review Letters. 136(14), 148203. Wassermair, Michael, Gerhard Kahl, Roland Roth, and Andrew J. Archer. “Navigating Complex Phase Diagrams in Soft Matter Systems.” <i>Physical Review Letters</i>. American Physical Society, 2026. <a href="https://doi.org/10.1103/nbvt-fgjy">https://doi.org/10.1103/nbvt-fgjy</a>. Wassermair M, Kahl G, Roth R, Archer AJ. Navigating complex phase diagrams in soft matter systems. <i>Physical Review Letters</i>. 2026;136(14). doi:<a href="https://doi.org/10.1103/nbvt-fgjy">10.1103/nbvt-fgjy</a> Wassermair, M., Kahl, G., Roth, R., &#38; Archer, A. J. (2026). Navigating complex phase diagrams in soft matter systems. <i>Physical Review Letters</i>. American Physical Society. <a href="https://doi.org/10.1103/nbvt-fgjy">https://doi.org/10.1103/nbvt-fgjy</a> M. Wassermair, G. Kahl, R. Roth, A.J. Archer, Physical Review Letters 136 (2026). Wassermair, Michael, et al. “Navigating Complex Phase Diagrams in Soft Matter Systems.” <i>Physical Review Letters</i>, vol. 136, no. 14, 148203, American Physical Society, 2026, doi:<a href="https://doi.org/10.1103/nbvt-fgjy">10.1103/nbvt-fgjy</a>. 217642026-04-26T22:01:47Z2026-04-28T07:03:48Z