@article{CTT100708488,
  author = {HIDETOSHI NISHIMORI and Manaka Okuyama and Yuuki Yamanaka and Marek Rams},
  title = {Anomalous behavior of the energy gap in the one-dimensional quantum XY model},
  journal = {Physical Review E},
  year = 2015,
}

@article{CTT100782955,
  author = {Junichi Tsuda and Yuuki Yamanaka and Hidetoshi Nishimori},
  title = {Energy gap at first-order quantum phase transitions: An anomalous case},
  journal = {Journal of the Physical Society of Japan},
  year = 2013,
}