{"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":"7367714e-8073-56b0-9cbe-5c2ed657958e","task_key":"train--Challenge~5f17~5fmain","task_revision_id":"1","upstream_id":"Challenge_17_main","short_description":"Consider the following Hamiltonian:…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the numerical value of S/N.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    S_per_N: float, The zero temperature entropy per particle, $S/N$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    S_per_N = ...\\n    # ---------------------------------------------------------------\\n\\n    return S_per_N\",\"problem_description\":\"# Problem setup:\\nConsider the following Hamiltonian: $H=-\\\\frac{1}{2}\\\\sum_{a=1}^N\\\\sum_{i,j,k,l=1}^N C_{ij}^a C_{kl}^a\\\\chi_i\\\\chi_j\\\\chi_k\\\\chi_l$, where $\\\\chi$ are Majorana fermions and $N^2\\\\langle C_{ij}^a C_{kl}^b\\\\rangle=J\\\\delta_{ab}(\\\\delta_{ik}\\\\delta_{jl}-\\\\delta_{il}\\\\delta_{jk})$. Consider the large $N$ limit. Define the zero-temperature entropy as $S= \\\\lim_{T\\\\to 0}\\\\frac{\\\\partial F}{\\\\partial T}$, where $F$ is the free energy of the system.\\n\\n# Main problem:\\n\\nCalculate the numerical value of $S/N$ to four decimal places.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}