{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"26a20460-a6bc-5854-a421-c9f4df58a2f8","task_key":"train--Challenge~5f28~5fmain","task_revision_id":"1","upstream_id":"Challenge_28_main","short_description":"Consider a four-dimensional hypercubic lattice with lattice spacing $a$ and…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the values of the exponents of the leading power law dependence on the Fermi momentum\\n    of the correction along $y$ direction per unit volume, the quasiparticle scattering rate\\n    and transport scattering rate on the Fermi surface in the zero frequency limit.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    exponent_correction: float, the exponent of the leading power law dependence on the Fermi momentum\\n        of the correction along $y$ direction per unit volume in the zero frequency limit.\\n    exponent_quasiparticle: float, the exponent of the leading power law dependence on the Fermi momentum\\n        of the quasiparticle scattering rate on the Fermi surface in the zero frequency limit.\\n    exponent_transport: float, the exponent of the leading power law dependence on the Fermi momentum\\n        of the transport scattering rate on the Fermi surface in the zero frequency limit.\\n    \\\"\\\"\\\"\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    exponent_correction = ...\\n    exponent_quasiparticle = ...\\n    exponent_transport = ...\\n    # ---------------------------------------------------------------\\n\\n    return exponent_correction, exponent_quasiparticle, exponent_transport\",\"problem_description\":\"# Problem setup:\\nConsider a four-dimensional hypercubic lattice with lattice spacing $a$ and nearest-neighbor hopping amplitude $t$. The system includes an on-site Hubbard interaction of strength $U$, and the chemical potential is near the bottom of the conduction band.\\n\\nThe Hubbard interaction will give a correction to the real part of the finite-frequency paramagnetic conductivity.\\n\\n# Main problem:\\n\\n\\nAt zero temperature, to the second order in $U$, what's the leading power law dependence of the Fermi momentum $k_F$ of this correction along $y$ direction per unit volume in the zero frequency limit? At zero temperature, to the second order in $U$, what's the leading power law dependence of the Fermi momentum $k_F$ of the quasiparticle scattering rate and transport scattering rate on the Fermi surface in the zero frequency limit?\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}